Skillet Chicken Pot Pie

Name: Skillet Chicken Pot Pie
Ingredients: 14 Tbs. (1 3/4 sticks) (7 oz./220 g) unsalted butter, cut into pieces; 1 cup plus 2 Tbs. (5 1/2 oz./170 g) all-purpose flour; 1/3 cup (3 fl. oz./80 ml) dry sherry; 2 Tbs. chicken demi-glace; 6 cups (48 fl. oz./1.5 l) chicken stock; 1 1/2 tsp. chopped fresh thyme; 1 bay leaf; 1 large yellow onion, chopped; 3 celery stalks, chopped; 2 carrots, peeled and cut into slices 1/8-inch (3 mm) thick; 3 oz. (90 g) button mushrooms, diced; 6 oz. (180 g) small red-skinned potatoes, cut into 1/2-inch (12-mm) dice; 3 cups cubed cooked chicken (about 1 1/4 lb./625 g); 1 cup (5 oz./155 g) fresh or frozen peas; Kosher salt and freshly ground pepper; 3 batches basic pie dough; 1 egg beaten with 1 tsp. water; Flaky sea salt for sprinkling