From the photo of the cakes on the other thread, I see the texture as kind of "medium" and not what I would call very coarse or open. It looks like an oil cake-based cake's texture (as you say, it reminds you of carrot cake). Muffins, too, are often made with a liquid fat -- melted butter or oil. The fat is not creamed; that's the important thing. If the recipe does have you cream the butter, you don't want to cream it very long. Many "regular cakes" end up with a texture not too far from your photo, though.
Very fine-textured cakes, like many in Rose Levy Beranbaum's The Cake Bible, aren't all that common, (and to some of us, too fine-textured).
So, it probably is an oil-base cake, but you can get close to that texture by other means. I thought it might even be a chiffon cake, a mid-century California invention that is an oil-based sponge cake, with a coarser texture than regular sponge cake. I never saw a recipe for one that had a brownish/caramel flavor, but I don't see why there coiuldn't be one.

Perhaps if you approach the mixing of the batter more like a muffin batter rather than a cake batter. Use the techniques for a "quick" bread rather than the longer beating done when making cake batter:

~ stir together the dry ingredients in a bowl

~ lightly combine the wet ingredients in another bowl

~ briefly mix the wet into the dry and mix only until no dry particles remain then pour the batter into the cake pans.

By contrast, I made a cake mix cake the other day that called for beating the batter for 4 minutes until it was very smooth.

Just had a thought, it seems I remember the texture of cakes made with Bisquick having a more open structure. Here is the coffee cake recipe using Bisquick:

2 cups Bisquick
2 TB sugar
1 egg
2/3 cup cold water or milk

Heat oven to 400F. Grease layer pan (or cupcake pans). Mix all ingredients with a spoon; beat well for 1/2 minute. Spread in prepared pan(s). Bake 20-25 minutes. For richer coffee cake, add an additional 2 TB sugar and 2 TB melted shortening or vegetable oil.

There are recipes on the web for making your own buttermilk baking mix if you want to do that.

Here is another cake recipe from Jiffy mix:

Jiffy Cake Recipe #43909 from Recipezaar

by ciao

30 min : 5 min prep

SERVES 10 -12 , 1 8-inch or 9-inch cake

* 1 1/2 cups jiffy mix baking mix
* 3/4 cup sugar
* 2/3 cup milk
* 1 egg
* 2 tablespoons soft shortening
* 1 teaspoon vanilla

1. Heat oven to 350°. Blend all ingredients, beat for 2 minutes.
2. Pour into lightly greased 8" pan.
3. Bake 25-30 minutes.

To cloudy and teresa: Thank you for your help. How does using cake flour DIFFER in the resulting texture vs. using A.P. flour in a cake? And teresa: what is Jiffy mix baking mix? Is this the same as Bisquick? (I'm in Ca.) I've only seen in the past from Jiffy small little boxes of cake mix (with sugar already added) but have never seen it referred to as a baking mix. Are these one in the same? And cloudy: I always thought that chiffon cakes were very tight and spongy with a lot of bounce - like the texture of (forgive me) Twinkies.

I didn't see your original thread but went and read it now. The frosting looks to me exactly like browned butter icing, which is often used as a glaze for doughnuts in PA Dutch cooking.

You brown butter in a small deep pan over medium high heat until it foams up. Then remove it from the heat and stir until the foam subsides. Repeat once or twice until the butter is a golden brown color, not a dark brown. If you're not used to making browned butter (which is also served over vegetables), it might take a couple of times to get it right.

Pour butter into a heatproof bowl, leaving the dark butter solids in the pan. Add a dash of salt, a squeeze of fresh juice, and sifted confectioner's sugar to acheive the correct texture. Add milk if frosting is too stiff. Pour or spread over the cakes and set aside to harden.

The cakes looks like an old-fashioned hot buttermilk sponge cake. Have you tried any recipes like that?

Arline,
I think that cake flour will give a much finer texture in the tea cake than perhaps what you want. Cake flour is milled finer than AP flour.

Jiffy is the same type of mix as Bisquick. The company that makes Jiffy has a line of different baking mixes - cake, corn muffins, pie crust, muffin, and "baking mix." You should be able to use Bisquick Buttermilk Baking Mix and Jiffy Baking Mix interchangeably. There is Pioneer brand baking mix also.

I find it hard to believe that there isn't a recipe for these tea cakes on the internet! Usually you can find any recipe on the web.

Thank you Ruthanna! That DOES sound like the glaze I am looking for. And yes, I am familiar with browning butter so this should be a piece of cake (pardon the pun). Oh, I'm excited bec. I DO think this is one part of the puzzle. No, I haven't even HEARD of hot buttermilk sponge cake, but will immed. go out there and look. However, as I have prev. mentioned, isn't sponge cake like the texture of Twinkies, which this cupcake clearly is not, or are there diff. textures of sponge that may have a similar texture to the rougher type of cake?

Teresa: thanks for that clarification on Bisq. vs. Jiffy. I think the reason I'm not finding the recipe for this is bec. I'm quite certain that the bakery CHANGED the name of their cupcake (to "tea cakes") in the 60s when they first started so that they couldn't be identified and then copied by others bakeries! They truly became famous for these during that era and were shipped all over Ca. & Las Vegas, according to an article I sleuthed out.

The frosting recipe should have read "a squeeze of fresh lemon juice" and I forgot to mention that you can add vanilla extract to the frosting but I usually don't. I like that sort of sweet, nutty flavor to come through.

Here's the buttermilk cake recipe I use, although it's much older than the 60's. It only makes a small pan so it's worth a try. If it's the wrong kind of texture, you can use it for strawberry shortcake or something like that.

HOT BUTTERMILK CAKE

1/2 cup buttermilk or sour milk
3/4 cup all-purpose flour
1 tsp. baking powder
1/4 tsp. salt
3 eggs, at room temperature
1 cup sugar
1 tsp. vanilla extract

Preheat oven to 350. In small saucepan, scald buttermilk. Remove from heat; set aside. In medium bowl, combine flour, baking powder and salt; set aside.

In small mixer bowl with mixer at high speed, beat eggs until thick and lemon-colored. Gradually add sugar, beating until mixture is smooth and blended, about 5 minutes. At low speed blend in flour mixture just until smooth. Add WARM buttermilk and vanilla, beating just until combined. Pour batter immediately into an ungreased 9-inch square baking pan.

Bake 25 to 30 minutes or until cake springs back when gently pressed with fingertip.

Good luck in your quest!