The cabinet below the cooktop has to be a 36" or larger for this to occur as it's walls support the weight of the granite. If that's already in place, then it's a filthy dirty mess that will require that you create a plastic tent around the whole area and use a vacuum while it happens. And you'll still be cleaning up abrasive dust from everything. It can get into your drawer slides and ruin them. I recommend using the very sticky Saran wrap to wrap them completely after you remove the drawers themselves. Yes, I'd do it to the entire kitchen. Did I mention that the dust goes everywhere?

It could cost anywhere from a couple of hundred dollars to a thousand or so depending on the auxiliary work needed to be sure the granite is properly supported or if it cracks during the cutting process and needs to be repaired with epoxy. No granite fabricator will take responsibility for the granite possibly breaking either. You'll have to sign a waiver stating that you were informed that was a possibility and that you hold them blameless should that happen.

There is indeed a 36" cabinet underneath. But it sounds like this is going to be a complete mess. Hmm...anything else I'm missing that I should consider before taking this kind of plunge?