This is a budget kitchen renovation I did using an Ikea corner cabinet and butcher block. I used thin finish plywood for the side and back of the kitchen island and it worked out well. i think you can call this an Ikea hack, but not sure, but for a few bucks you can have a new kitchen island. Be sure to treat the butcher block with the wood preservative Ikea sells several times before installation.
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Step 1: Plywood Finish
I used a thin finish plywood, which I primed and then 2 topcoats. Don't cheap out on the paint you use, you get what you pay for with paint and this is a kitchen. We used a nail gun with brad nails to set the plywood in place.
The frame we built where the butcher block cantilevers out is with 2x3s, be sure to screw this into the subfloor.
The dishwasher should come with a foil tape strip that goes on the underside of the wood countertop, just above the dishwasher door. This strip helps keep the moist air from the drying cycle of the dishwasher from warping the wood counter.