Joe will have to weigh in on this one, but my guess is that either cut-out (cooktop or range) will require that you support your overhang somehow. May I ask why you are averse to supports?

I don't think I am averse to supports. With supports this would be possible?

I could probably do something like this pretty easy considering there is an existing wall there...

http://swoodwork.com/wp-content/uploads/island_wood_counter.jpg

I'm not an expert, so please take this with a grain of salt 'till the cavalry arrives. My bet is that you will want to go this route instead, but I have no idea what you would do with the cut-out areas and that probably depends in part on what type of counter material you are using. Joe (Joseph Corlett) is the pro, and he is generous with his knowledge. I'm sure he'll check in soon.

If you don't want any knee-knocking corbels, I'd have a custom frame fabricated and installed. If you use engineered stone as a countertop, you can cantilever up to 15" with no additional supports. You'll want a larger overhang anyway.