Begin by preheating your oven to 375 degrees F and preparing the pastry. Roll out 14 ounces of good-quality puff pastry on a lightly floured surface with a floured rolling pin, then transfer it to a parchment-lined baking sheet.

Cover with plastic wrap and refrigerate while you prepare the filling. Next, combine 4 cups of chicken broth with 1 large yellow onion cut in quarters, 2 dried bay leaves, 1 teaspoon whole black peppercorn, and 3 sprigs fresh thyme in a large pot over high heat.

Bring the broth to a boil, then reduce heat and simmer for 30 minutes. Add the 4 chicken breasts, raise the heat to return the mixture to a boil, then reduce heat again and simmer until the chicken is cooked through, about 10 to 15 minutes.

Transfer the chicken to a plate to cool, strain the stock and reserve 2½ cups for the filling, then cut the cooled chicken into bite-size chunks.

In a large sauté pan, melt 3 tablespoons of unsalted butter over medium heat. Add ½ cup of peeled white pearl onions and 2 medium diced carrots, cooking for about 5 minutes while stirring occasionally.

Add 1 cup of sliced white mushrooms and 1 cup of peas, cooking for another 5 minutes. Stir in 5 tablespoons of all-purpose flour and cook for one more minute. Pour in the reserved stock and 1 cup of milk while stirring constantly, cooking until the sauce thickens, about 5 minutes.

Remove from heat and add the cooked chicken, 1 tablespoon chopped fresh thyme, 1 teaspoon salt, and ½ teaspoon fresh ground black pepper. Divide the chicken mixture among four 2-cup individual oven-proof bowls.

Remove the pastry from the refrigerator and cut four circles using the empty bowls as a guide. Place one circle on each bowl and press around the edges to seal.

Cut a vent in the center of each pastry lid, then brush each with 1 lightly beaten egg using a pastry brush. Bake until the pastry is puffed and dark golden brown, approximately 35 minutes, then serve immediately.