Preheat oven to 425 degrees.
In a large Dutch oven or enameled cast-iron casserole, melt 2 tablespoons of the butter. Add the shallots, mushrooms and carrot chunks and cook over moderate heat, stirring, until the shallots and mushrooms are softened, about 8 minutes.
Add the wine and cook until completely evaporated, about 1 minute.
Stir in the 1 tablespoon of flour and the broth and bring to a boil. Season with salt and pepper. Simmer until thick, about 3 minutes.
Stir in the chicken and peas. Simmer while you make the toppings.
In a food processor, combine 1 1/4 cups of flour, 4 tablespoons of butter, and the chopped sage and thyme. Pulse 5 times.
Add the milk and pulse just until a soft dough forms.
Using a tablespoon, or your hands, place 20 balls of dough over the chicken stew.
Bake in the center of the oven for 25 minutes.
Turn on the broiler and broil for 1 to 2 minutes, until the biscuits are golden.
Let rest for 5 minutes before serving.
Servings 0