High Bar support

We are to the point in the kitchen redo where cabinets are about to go in. We finished rewiring with GFCI outlets, ran dedicated lines for all required appliances and covered the walls in beadboard paneling. Floors are going in soon, they are Ellerton laminate. I know, not the best, but doable until we have kids. We found some plans to make our own base cabinets out of plywood and 2x4's, and we plan to make them all over the next week or two.

On the back side of the kitchen, there is going to be a 30" stove, 8' of cabinets including the sink, then a corner cabinet with 5' of cabinets jutting out into the room to divide the living room from the kitchen. On the living room side of the peninsula, i want to put in a high breakfast bar. It will have the same laminate countertop that the rest of the kitchen will. The base of the high bar will be covered in beadboard, as well as the end of the bar and peninsula that will be visible from the living room.

Sorry about the novel. My question is, what kind of support do i need to put on the back of the peninsula cabinets to hold up the bartop? Can i just make a row of vertical 2x4's, like a half-wall, then use cornices to support the bartop? There will be no drywall on it.

There are no pictures because i have not actually built these cabinets yet.