Chicken and Biscuits in a Pot

Name: Chicken and Biscuits in a Pot
Ingredients: 6 tablespoons unsalted butter; 2 shallots, thinly sliced; 1/2 pound shiitake mushrooms, stemmed and thinly sliced; 1 large carrot, cut into 1/3-inch chunks; 1/2 cup dry white wine; 1 1/4 cups plus 1 tablespoon self-rising flour; 2 1/2 cups low-sodium chicken broth; Salt; Freshly ground pepper; 3 cups shredded rotisserie chicken; 1/2 cup frozen baby peas; 1 tablespoon chopped sage; 1 tablespoon chopped thyme; 1/2 cup plus 2 tablespoons whole milk