^ Fill it full of wood glue first please.

Cabinet cracked when the slab was installed? Cabinet may not be supported properly (cabinet installer issue) or floor may be weak, exposed by weight of slab which isn't the slab installers responsibility, but it happens.

Can we get a shot of the side please? This can be fixed to nearly invisible, but if it was caused by a nail, it would be better if the nail was pulled out.

You can probably just clamp and glue this back in, but I would want the couter people to pay someone to do that.

I believe the split is due to a vertical screw (nail?) that has been used to attach the plywood, not due to the weight of the granite. With the screw in there, it won’t push back together.

Here are two more pics. The larger looking boards are false doors not attached to that piece of wood.

Tap the cabinet front off please. Yes, the wood may cleanly split more, but that's a small tradeoff as opposed to pulling the granite from the substrate without cracking it. A cabinet repair that's not at eye level is much more inconspicuous than a granite repair that is. That'll make repairing the cabinet front easier too. The screw has got to go. Hopefully they used cheap drywall screws which will snap easily.

What happens if the screw stays in? I had someone take a look and they said the same thing, that the screw should be taken out to make the best repair, but that wood glue would keep it from splitting more. Do you mean just the chunk on the right? With the way the peninsula is put together it doesn’t look like the whole front will be possible to remove.

Can you take a picture of the back side of the face from the inside of the cabinet? If we can figure out how the face is attached we can probably tell you how to fix it better.

With any luck it is attached with pocket screws from the inside. Also, does every cabinet have its own face frame? If you can’t tell, snap a picture of the other side where the cabinets join.

You can repair it with the face frame attached if you have to, but if you can get it off, the repair will disappear for sure.

I wouldn't try to get that screw out, you or whoever will be doing that will make it even worst and cause more damage to the cabinet... order a touchup kit from the cabinet manufacturer (if it didn't come with the cabinets or you can easily find one to match) and to do the best possible match, it shouldn't be to hard to fix that.

From afar that crack is not as big as it seems in a close-up image nobody will notice it @ that location if you don't tell anyone.

As the fabricator goes or installers whoever got the check, they're responsible for that, some of these guys are in a rush they do not take the time to pre-drill anything, and everything is rushed because they want to do 2-3 installs a day.

Try to get a few $$$ back make it sound like it's a big deal to fix it and fugget-about-it.

Good luck

^ Much lower risk; not a bad idea.