Place the chicken in a stockpot with carrot, onion, celery, leek, parsley, thyme and bay leaf and chicken stock to cover. Simmer 1 1/4 hours uncovered. Strain and reduce the stock to 3 cups. Remove the chicken from bone and dice into 1-inch pieces. Discard skin, bones and vegetables.
Blanch the peas in boiling salted water 1 minute. Remove and cool. Blanch the carrots 3 to 4 minutes. Drain and cool. Cook the mushrooms in 1 tablespoon butter over medium high heat 3 minutes. Reserve.
Melt 3 tablespoons butter in a saucepan. Add 4 tablespoons flour and stir constantly 2 minutes. Whisk in the reserved stock and cook until it thickens, 5 minutes. Season with salt and pepper. Add the diced chicken, peas, carrots and mushrooms. Place in a 1 1/2 quart casserole.
For the biscuits, sift the flour, 1 teaspoon salt and baking powder together in a bowl. Rub butter into flour, picking it up and dropping it far above the bowl to incorporate air, until it resembles coarse meal. Add buttermilk until it holds together. Form into a mass and roll it quickly on a well-floured surface. Fold it in half and roll again. Repeat, rolling it out to 1/2" thick. Using a 2" round cutter, cut 12 biscuits and fit them close together on top of stew. Bake in a 400 F oven 20 to 25 minutes until biscuits are golden and stew is bubbling.
Serve the stew with two biscuits per person.