Chicken Pot Pie

From "The Comfort Table" by Katie Lee Joel.

one 14-17 oz. puff pastry
1 qt. low sodium chicken broth
1 large onion, quartered
2 bay leaves
1 tsp. whole black peppercorns
3 sprigs fresh thyme, plus 1 Tbsp. chopped
4 boneless, skinless chicken breast halves
3 Tbsp. unsalted butter
1/2 c. peeled fresh pearl onions (I used frozen)
2 med. diced carrots
1 c. sliced white mushrooms
1 c. thawed frozen peas
5 Tbsp. flour
1 c. milk
1 tsp. kosher salt
1/2 tsp. pepper
1 large egg, lightly beaten

Combine broth, onion, bay leaves, peppercorns and thyme sprigs in a large pot over high heat. Bring to a boil, reduce heat and simmer 30 minutes. Add chicken breasts. Raise heat and return to a boil. Reduce and simmer until chicken is cooked through. Transfer to a plate. Strain stock and set aside 2 1/2 c. Cut chicken into bite size pieces. Preheat oven to 375. Melt butter in a large skillet over medium heat. Add pearl onions and carrots. Cook, stirring occassionally, for about 5 minutes. Stir in flour and cook 1 minute more. Add reserved stock and milk, stirring constantly. Cook until sauce begins to thicken, about 5 minutes. Remove from the heat and add chicken, chopped thyme, salt and pepper. Spoon into baking dish. Using a pie dish as a guide, cut the puff pastry in a circle and place over the filling. Cut a vent in the center and brush with beaten egg. Bake about 35 minutes.