Cabernet Braised Short Ribs with Chard and Orecchiette

About 4 lbs. meaty short ribs, excess fat trimmed

Kosher salt and freshly ground pepper

olive oil, divided

coarsely chopped onion

coarsely chopped carrot

coarsely chopped celery

garlic, minced, divided

tomato paste

bottle cabernet sauvignon

sprigs fresh parsley

springs fresh thyme

bay leaf

chicken or beef stock

pasta shapes, such as orecchiette

finely chopped onion

bunch Swiss chard, ribs removed and coarsely chopped

Freshly grated Parmesan, for serving