It's certainly doable, but not DIYable unless you are a granite fabricator and metal fabricator. You will need to remove the drywall in order to be able to firmly attach metal brackets to the studs. The most supportive would be T shaped plates on either side of the stud (bolted together through the stud) with the T projecting outward be 1/2" rod steel. Then reapply the drywall, leaving only the rod steel protruding. The granite fabricator would then need to fabricate a 3 cm slab to your style specifications, and drill the 1/2" holes into the granite at the specified locations. The granite would then be slid onto the steel, and caulked at the drywall/granite juncture.