Chicken and Dumplings

bone-in-skin-on chicken parts

Kosher salt and freshly ground black pepper

vegetable oil

bay leaf

thyme sprigs, or 1/2 teaspoon dried thyme

rosemary sprig, or 1/2 teaspoon dried rosemary

butter

large onion, cut into 1/2-inch dice

large carrots, cut into 1/2-inch dice

celery stalks, cut into 1/2-inch dice

all-purpose flour

large potato, peeled and diced

heavy cream (optional)

large egg

milk

butter, melted

all-purpose flour

baking powder

kosher salt

Italian parsley, chopped, for garnish (optional)