Ingredients:
Pie Dough: Slightly toast ½ the rosemary and thyme. Dust a clean, dry work surface with flour and place the puff pastry over top. Sprinkle the pastry with flour, herbs, and roll to about ⅛-inch thick, smoothing the creases with the rolling pin at the same time. Cut out 4 circles about 2 inches larger than the diameter of your soup bowls. (Alternatively, cut out 6 circles if making smaller portions.) Place the dough rounds on the foil-lined baking sheet and refrigerate until ready to use. Preheat the oven to 425°F and set the oven rack to the center position.
Filling: In a large sauté pan over medium heat, melt the butter. Add the yellow onion, garlic, celery, and carrots, rosemary, and thyme. Sauté, stirring occasionally, until the carrots are just cooked, 8 to 10 minutes. Remove herbs and add the flour and cook, stirring constantly, for about 2 minutes. Add the broth, salt, and white pepper. Bring to a boil, scraping the bottom and corners of the pan to incorporate the flour and simmer until thickened. Off the heat, stir in the heavy cream, thyme, chicken, and peas. Taste and adjust seasoning, if necessary. Ladle the filling into 4 large or 6 small oven-safe soup bowls. The filling should come up no more than three-quarters of the way to the top of the bowls. Beat the egg with 1 tablespoon of water.
Remove the dough rounds from the refrigerator. Brush the outside edges of each bowl with the egg wash. Place the cold dough rounds over the bowls, pressing firmly around the edges so that the dough adheres. Transfer the bowls to a foil-lined baking sheet. Brush the dough with the egg wash. Using a sharp knife, make a ½-inch slit in the top of each pie. Place the bowls on the foil-lined baking sheet and bake for 20 to 25 minutes, or until the pie dough is a rich golden brown.
