Braised Chicken with Figs without dijon butter

4 chicken breasts salt black pepper 4 tablespoons butter 2 tablespoons vegetable oil (Olive oil works good, too) 1 carrot , scraped and cut into 1/2 inch wide[...]

8 bone-in chicken thighs , skin removed 1 1/2 teaspoons kosher salt , divided fresh coarse ground black pepper 1 tablespoon olive oil 2 large sweet onions ,[...]