I don't know that miso would aid in emulsifying it and it surely will change the taste.
Try about a tablespoon of either egg beaters....which are pasteurized liquid whole eggs, or about 1/2 teaspoon of powdered egg.
I wonder if powdered egg white would work? I always have that around.
I think you need a little more oil than 1/4 cup. The usual ratio is twice as much oil as vinegar. And what kind of vinegar are you using? I like rice vinegar for something like that.

You could add a tablespoon of mayonnaise to emulsify it, and for an Asian flavor, you can use Kewpie Mayo.

If you add Miso, you will be making a miso salad dressing, which is something altogether different, as Linda said, but I make that also.

lindac92, the recipe calls for regular vinegar but next time I'll try rice vinegar. Would you suggest increasing the amount? I reduced the oil because the original 1/2 cup made the dressing very greasy since it would immediately separate. I don't think my mother had this problem so I'm wondering if an ingredient might be missing from the recipe?

Lars, I thought adding a little miso (1 -2 Tbs?) would not alter the flavor too much. I've got some Kewpie Mayo and will try that, although wouldn't it change the "Asian" flavor more so than miso would?

Thanks for the suggestions!

Do whatever it takes to make the oil to vinegar ratio 1 to 2.
For a simple dressing like that I often do a "toss and dump"...Have your salad in a bowl, drizzle on the oil and toss, add a little more oil and toss until every leaf is coated, add a little vinegar and toss.....salt and pepper and sugar....toss....taste a leaf....add more of what it needs. There should be no dressing in the bottom of the bowl....only add what is needed to coat the leaves.
You could use all sesame oil if you use that method.

lindac92, doesn't the oil make the cabbage limp and translucent and then not able to be coated with the other ingredients? Even with half the original amount of oil I find a lot of the dressing sitting in the bottom of the bowl, even using just half the dressing. This is the reason I want to add an emulsifier.

Miso has a very intense flavor - mayo does not, and so miso would change the flavor more than mayo, but you may still like it - it just will not be the same salad dressing. The only added ingredient in mayo would be the egg element, and you could add a bit of egg yolk to the dressing as an emulsifier, but since the quantity of the dressing is so small, you would not need a whole egg yolk. Alternatively, you could double the recipe and use a whole egg yolk, and then save the leftover salad dressing for the next salad. If you add egg, I recommend making the dressing in a blender instead of shaking it, and you will end up with a dressing that is very similar to mayonnaise, which may be too thick. Adding a small amount of mayo at a time may help emulsify the dressing without making into full-fledged mayonnaise.

Oil doesn't make cabbage limp....salt, sugar and vinegar do. The the oil coats the cabbage and when that has happened the salt and sugar won't get on the cabbage, but will stick to the oil on the cabbage.
I hate a soggy salad.....and when there is dressing sitting in the bottom of the bowl the salad is soggy and over dressed. Maybe that's why you think it's too oily....you are adding too much dressing.

Lars and lindac92, thanks a bunch! I learn something new every day...keeps me going!

A "classic French dressing"...whatever that is determins the ratio. The thought being that the oil carries the flavors and the essential oils of the spices....and that the oil aids in the digestion and absorbtion of the vitamin A in the salad.
But....whatever floats your boat. One of my favorite dressings is simply honey thinned with lime juice and spiced with lots of fresh ground pepper.