If using chicken breasts, poach them in lightly salted water until fully cooked, about 12–15 minutes, checking that the thickest part reaches 165°F. Let cool slightly, then shred into bite-sized pieces and reserve 1¾ cups of the cooking liquid. If using rotisserie chicken, shred the meat and use chicken broth instead of the cooking liquid.

Melt the butter in a large saucepan over medium heat. Add the onion and celery and cook for 4–5 minutes, until softened.

Sprinkle in the flour and stir constantly for 1–2 minutes. Stir in the garlic powder, celery seed, black pepper, salt, and chicken bouillon paste.

Gradually whisk in the reserved chicken cooking liquid or broth, followed by the 1 cup whole milk. Stir until smooth and thickened, about 3–4 minutes. The sauce should coat the back of a spoon.

Fold in the chicken and frozen mixed vegetables, then remove from the heat. Let the filling cool for 15–20 minutes, or until it is no longer hot, before assembling the pie.

Preheat the oven to 425°F. Roll out the bottom pie dough and fit it into a 9-inch pie dish. Add the cooled filling, then cover with the puff pastry or additional pie dough. Seal and crimp the edges and cut slits in the top for steam to escape. Whisk the egg with the 1 tablespoon milk and brush over the top crust.

Place the pie dish on a baking sheet to catch any drips. Bake for 40–50 minutes, until the crust is golden brown and the filling is bubbling. If the top browns too quickly, loosely cover it with foil for the remaining baking time.

Let the pot pie rest for 15 minutes before slicing and serving.