How can I build a table into an alcove?
I would just buy a 1x4 or similar material that would go with your butcher block and use them as a ledger board on the three sides.  Simply measure the height you want, attach ledger board to wall all the way around (3 easy cuts) and attach them to the studs.

Then just slide on your butcher block.  To attach to ledger you can use screws but a little silicone is probably more than enough for a tight space to keep it from moving.