Braised Chicken and Vegetables

2 tablespoons butter , divided 2 chicken breast halves , bone-in, skinned 2 chicken thighs , bone-in, skinned 2 chicken drumsticks , bone-in, skinned 1/2[...]

1 tablespoon olive oil 6 bone-in chicken thighs 1 potato , peeled and chopped 1 yellow onion , finely chopped (1 cup) 2 carrots , chopped 2 garlic cloves ,[...]