Mine is plywood because we had to have a rough top. Is it supposed to be finished underneath? I am talking about the place where the counter stools go.
Mine is 3 cm granite, so no need for plywood. The stone is NOT finished. My ILs have an island with overhang-plywood, peeps of stone, screws for the things that connect to the island itself--so, to answer the question--underneath is NOT finished or pretty.
Mine is 2 cm quartz with a built-up edge on top of 5/8" plywood. My old cab boxes were painted in-place and looks like they also did the underside of the plywood. I don't remember asking them to do that. Back in the day when I had a tile counter, the plywood was just left unfinished, pretty ugly.
Mine isn't finished.
Maybe I'll give it a quick paint like kirkall. I was thinking of letting my kids, friends and guests sign it and draw there like a secret living guest book. You can't see it unless you crawl under there or really try.