PREHEAT OVEN AND PREP PUFF PASTRY: Preheat your oven to 400°F. Unfold the puff pastry and let it rest on the counter until slightly softened and easier to cut.
SWEAT THE VEGETABLES: In a large stockpot, melt 4 tablespoons (½ stick) unsalted butter over medium heat. Add 1 small yellow onion, 3 medium carrots, 3 ribs celery, and 1 large Russet potato. Add half of the salt. Sauté for 3 to 4 minutes, until the onion turns translucent and the vegetables begin to soften. You should smell the sweetness of the vegetables as they warm.
ADD FLOUR, PEPPER, REMAINING SALT, AND HERBS: Sprinkle in 4 tablespoons all purpose flour, ½ teaspoon fresh ground black pepper, the remaining salt, 1 teaspoon chopped rosemary, 2 teaspoons chopped thyme, and 1 tablespoon chopped parsley. Cook for 2 to 3 minutes, stirring often. The mixture will thicken and smell warm and nutty as the flour toasts.
ADD LIQUIDS AND CHICKEN: Pour in 1 ½ cups whole milk, 1 ½ cups chicken stock, and ½ cup heavy cream. Stir well, scraping the bottom of the pot. Add ½ cup frozen peas and 2 cups diced cooked chicken. Increase heat until the mixture begins a gentle simmer.
SIMMER UNTIL THICKENED: Simmer for 5 to 10 minutes, stirring occasionally, until the vegetables are tender and the filling thickens into a creamy gravy. Drag a spoon across the bottom of the pot; the trail should slowly close. Taste and add a pinch more kosher salt if needed.
CUT PASTRY TOPS: Place an oven safe bowl upside down on the puff pastry to measure. Cut circles about ½ to ¾ inch larger than the bowl so the pastry can drape and puff.
ASSEMBLE POT PIES: Spoon the hot filling into oven safe bowls. Lay a pastry round over each bowl and gently press around the rim to seal. If the pastry is thick, cut one small steam vent in the top.
BRUSH WITH EGG WASH: Whisk 1 large egg with 1 tablespoon water. Brush a thin, even layer over each pastry top.
BAKE: Bake for 15 minutes, until the crust is puffed and a deep golden brown. Loosely cover with foil and continue baking for 15 minutes longer, until the filling bubbles gently around the edges.
REST AND SERVE: Let the pot pies cool for 5 minutes before serving. The filling will be very hot and will thicken slightly as it rests.
Notes
Make Ahead: The filling can be made up to 2 days ahead or frozen up to 3 months. Thaw overnight before assembling.Storage: Store leftovers covered in the refrigerator for 2 to 3 days.Reheating: Reheat at 350°F for 15 to 20 minutes. For a single serving, microwave on 50 percent power for 1 to 2 minutes, then crisp the top if desired.Freezing: Freeze assembled, unbaked pot pies for up to 3 months. Bake from frozen at 375°F for 45 to 55 minutes. Cover with foil if the crust browns too quickly.Ingredient Tips: Fresh herbs give the best flavor, but if using dried herbs, use half the amount. Add corn or green beans with the peas if you want extra vegetables.Crust Options: KFC pot pies do not have a bottom crust. You may add one using refrigerated pie crust. If using pie crust instead of puff pastry, cut vent slits before baking.