How do I install a countertop with a large overhang without using a corbel or post?
I have gone through this on about 20 installs and have gotten better from my first ones.   The thicker the L-bracket the better.   A lot of time the big box doesn't sell ones that are made for countertop jobs.   This is something I usually order online because I get these cheaper and better quality.

I am going to give you pointers based on you making these as invisible as possible without the granite company scribing for them.   For the granite installer to do this you would have needed to be set up during their measurements.   They could have a "wide" scribe but I wouldn't go this way.

Steps:


Take current countertop off cabinet.
Take drawers or anything else out and out of the way.   
On the top of your cabinets where the L bracket is coming out cut out a indentions so that your L bracket is level with the top of the cabinet.   
Even with the bottom of the cutouts you are going to install a 2x4 (or 6) across the back inside of the cabinet.   
Great to get screws on this but I have used liquid nails before.   (prop it up while glue dries if you go this way)
Test it out.  Make sure that L bracket is level and lines up (you can do this before glue dries if glueing) - you are installing the L bracket inside the cabinet.
Do not screw in L brackets!!!
When countertop guys arrive set the L brackets in place and let them install counter on top of them.   This will assure they are positioned to support the counter.   You could be microns off and will need to support that with a shim on the 2x side.   
Use a rubber shim if needed (seen wood shims fall out), and screw it in.   
Your installers may want you to epoxy the counters to the L bracket... don't.   This does nothing but make it harder to uninstall.   


Note for your install you want it out about 10-12 inches - I will say 12 to be safe.   12 inches plus 1.5 inches for 2x plus .5 inch misc.... means you need a 14" L bracket.   I suggest you hit the side of the L bracket with an angle grinder on the corners facing the seated people to curve them out.

Also you want these about 6 inches from edges - can get away with 8 inches - you are really right on the edge of needing three brackets and someone doing a conservative install would use three.   



Edit for one-off challenges:


  
  It is on the end of the island.
  


This should be installed the same way if possible.   


  
  I have a sink that is going to take up a lot of room.
  


I have installed A LOT of undermount sinks...  If I install them the way I want to I brace them with 2x4s.   I could take a picture of my kitchen undermount in my home and I have a 2x4 on each side.   Why?   Usually you have about 2" of play on each side (I actually put the 2x4 after install/caulk - so about 2 days after).   For normal big double basin undermount you will get that 2 inches.   Given your sink is big if you put a lot of stuff in it (water) the caulk will not be able to hold it up.  Caulk is a really a lazy way for granite guys to hold sinks up anyway.  I actually first thought of doing this on one my installs after one of my sons was born the wife wanted to use sink to wash baby...   

I calculated about 40-50 pounds in the sink.   So being paranoid I added the 2x4s.   I have done this is 20+ kitchens with zero failures when before I had people calling up about caulk failing and shaky sink.   So get these in there if you can, helping you brace your L bracket is just a plus.   


  
  I really don't have room because of sink or drawers.
  


This is OK and have ran into this issue because of drawers.  Time to get your creative juices going.   What we have done in the past is router a 2x4 with beveled edges and some patterns and installed it as a decorative edging to the top outer part of the cabinet.   You won't even see it unless you bend down and look under the island and it is basically the exact same install as up above - albeit you will have to chisel out the top for brackets, you will need 1.5" less length on L bracket and your island actually isn't overhanging as much.   I would say the minimum depth here is 1" plus island backer if you don't want to go with 2x4 - the "deluxe island L brackets" might call for 1.5" though.   


  
  Can I use a T bracket?
  


Yes yes yes.   T-brackets are better than L brackets because they do a better job innately at making sure the supported material is aligned to the bracket.   Like I mentioned above you will probably have to shim to get your L bracket aligned.   You would have to do the same thing with the T-bracket but it will force you to shim where the L-bracket will just move to whatever is pushing the most.   The reason it was not mentioned is that the question involved installing a sink, and you would not be able to use a T-bracket.   Also it is much harder to find a quality T-bracket for countertops, especially longer ones.