Preheat the oven to 400 degrees F.
Carefully unfold one sheet of puff pastry on a floured surface. Using a rolling pin, roll out the pastry large enough to cover the bottom of 9-inch pie plate with overhang (about 12 inches in diameter). Trim the overhang, and using the tongs of a fork, prick the bottom of the pastry all over.
In a saucepan over medium-high heat, melt the butter. Add the carrots, celery and onions and cook until the vegetables start to soften, about 5 minutes. Stir in the flour and cook for 2 minutes, stirring constantly. Slowly add the broth and milk. Bring to a boil, reduce to a simmer and cook until the mixture thickens enough to coat the back of a spoon.
Stir in the turkey, peas, celery seed and season with salt and pepper. Remove from the heat and cool completely.
Unfold an additional sheet of pastry on a floured surface and cut into 6 to 8 even strips.
Pour the filling into the pie crust. Create a lattice pattern over the top by weaving the strips over and under each other. Trim the excess edges. Gently beat the egg and 1 tablespoon water in a small bowl. Brush the dough with the egg wash before placing the pot pie on a sheet tray.
Place in the oven and bake until the pastry is golden brown and the filling is bubbly, 45 minutes. Cool for 10 minutes before serving.
Recipe courtesy of Kelsey Nixon