I have a unique problem.  I needed to replace my cooktop.  After
consulting an appliances dealer, I still ended up with a smaller unit.
 I had to install it since the new cooktop could not be returned.
I could only find a similar granite to patch up the gap.  But the
mismatch really bothers me.  I can now find the matching granite.  I
need to know if it is possible to replace the mis-matched piece with
the matching piece and exactly how to do it, what to use to bond with
the minimum appearance of the original bigger cut-out.  Thanks.

I am not so sure how to repair the granite.  However if you have a
stainless steel cooktop what i have done is get a flat piece of
stainless made up that has an inside cut out to match your cooktop
size and an outer cut out to cover your existing slot in the bench. 
You will be surprissed how much it will look like it is part of the
cooktop.  Good luck with the granite but if it doesn't work out maybe
this will help.