This is old, so you likely don't need the information anymore but in case anyone else is reading and does...many quartz manufacturers don't require a support for an overhang of 13". Granite however, is a different story.
If you end up needing support, they have an item called a Stealth Brace that gets cut into the top of the cabinetry (before countertop install) that can support larger overhangs. They are essentially a thick piece of metal with holes drilled in it for attaching.
https://www.richelieu.com/ca/en/category/furniture-equipment/wall-shelf-supports/shelf-brackets/stealth-brace/1057923?s=stealth+brace
You'll only be able to see them when you're eye level is below the countertop.
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