¼ cup olive oil
4 Tbsp unsalted butter, divided
1 med onion, finely diced
2 large carrots, grated or cut into matchsticks
1½ lbs boneless, skinless chicken thighs, trimmed and cut into 1" pieces
2 tsp salt (we used sea salt), divided
¼ tsp black pepper, freshly ground
2 bay leaves, optional
1 cup dry white wine such as Chardonnay
5 cups hot low sodium chicken broth
2 cups medium grain rice such as Jasmine rice (un-rinsed)**
1 head garlic
⅓ cup fresh Italian parsley, finely chopped
½ cup shredded parmesan cheese, plus more for serving