First is that a post connected to the pony wall, is that why theres a pony wall in that spot ? b/c from your pics I cannot see any reason whatsoever that its of any use[ the wall] I think I would have had the cab finished on the end and eliminated the wall. Another question what about this concrete floor? what kind of finish is it going to get? it appears you have wood floors, A pro could patch that section if a gap occurs. Lets hope someone comes along that figure something out

The post is independent. The pony wall has electrical in it and was part of a fridge enclosure, which was demo'd to open up the kitchen. The kitchen has cement floors with radiant heat the dining room behind it has wood floors. It would be almost impossible to finish that portion of the floor and have it the same color as the rest of the cement in the kitchen as it is on a raised subfloor (not polished slab).

Will do.. what top should i do on top of the pony wall? Will post a photo after its done. I actually had white counters that were installed and had them removed and now going with grey counters. Let me know if I am making a mistake! What color should I go with if so? Pictured are the previous counters? Stick with them?

If you're redoing the countertops and don't mind spending more money, you could replace the pony wall with a fluted base column that's wide and deep enough to cover the flooring gap.

I am confused about what this product is. Sorry for my ignorance. Is this a fascia piece that attaches to the pony wall the mimic the grains of the cabinets or something else? My house is a mid century modern style with open ceilings so a faux support beam would rise about 30 feet

when you say build up and put counter to the end of it..

do you mean build up the drywall to counter level then put the quartz to the end of the wall and create a piece that covers the portion in front or build it up and run the quartz to the threshold?

@Barry Kruol No this would replace the pony wall and yes it'd mimic the cabinet stain. It's basically a double sided dishwasher end panel, if that makes sense?

Typically the columns are used to pull out sinks or stoves to set it apart. Does this show it better?

http://www.kraftmaid.com/base-fluted-column/

http://cloudcomputingjournal.com/32706/peachy-kitchen-sink-cabinet-with-dishwasher/

http://ejhcabinets.com/content/dishwasher-wall-fluted-column

https://www.pinterest.com/pin/341288478002381275/?amp_client_id=CLIENT_ID(_)

Though the cost isn't insignificant. Removed.

Interesting challenge Barry. I'd agree with Weil Friedman and Kerry Blossom above. Raise the pony wall about 4" or so and put a cap on it - (1" or thicker material cap and trim below to cover up the rise. I'd consider how to make this all with the post as a unified feature. Your quartz counter would terminate in same place as your white quartz photos above.

Also don't know if it works for your layout, but an end wall like that can be an interesting place for a shallow bookcase / open display shelves. It looks like you have enough passage width. That would give the wall cap a greater purpose for being there (makes it wider). You'd route that existing outlet in the backsplash created by your 4" rise facing the counter. Just another possible idea. Good luck!

Keep the drywall on the cabinet side of the pony, remove the rest of the drywall from the pony, add lumber to the height of cabinet, new drywall, countertop to extend over the pony.