If I get the soapstone countertop it's a solid slab about 1.25" (unlike granite that would be 3/4 inch with a lip of an additional 3/4). Does it sit right on top of the frameless cabinets or is there a base of plywood underneath? If there is a base of plywood doesn't it show? does the edge need to be finished? It would then make the counter 2 inches thick and I would need to adjust the cabinets so they aren't so high. What is the convention for how this works?

Thanks. I'm getting a bit overwhelmed by all the details to consider.