Preheat oven to 400°F.
Melt butter in an 8-inch ovenproof skillet over medium heat. Add leeks and carrots and cook until softened, 4-5 minutes. Stir in garlic and cook for an additional 30 seconds.
Stir the flour into the vegetables and continue to cook for 30 seconds while stirring. Stir in the stock, cream, salt, thyme, and pepper. Turn the heat up to medium-high to simmer the filling and thicken it to almost the consistency of a thick pot pie (it will continue to thicken as it bakes!) Taste and adjust for seasoning.
Stir cooked chicken, frozen peas, and parmesan into the mixture and remove skillet from heat. Allow to cool slightly.
Place pie dough over the skillet and use sharp kitchen shears to trim the dough, leaving a 1/2-inch overhang (it will shrink as it bakes). (Throw excess away, or cut it into little squares, sprinkle it with cinnamon and sugar and bake it!) Cut two 2-inch slits in the middle of the pie dough to allow steam to escape. Brush pie dough with a little heavy cream and sprinkle with flaky salt and freshly cracked pepper
Place skillet on a baking sheet to catch any drips and bake for 25 to 35 minutes, or until pie crust is golden brown. Different pie crusts will take different amounts of time, so start checking on it at the 25 minute mark.
Use a big spoon to dish the pot pie into two shallow bowls. Enjoy!