Sauté the Onions, Carrots, and Celery: In a large sauté pan, melt the butter. Stir in the onions, carrots, and celery. Cook until the vegetables start to soften and the onions are translucent.
Add the Garlic and Potatoes: Stir in the garlic and potatoes. Cook for 30-60 seconds until fragrant.
Add Flour: Sprinkle the flour over the vegetables and cook until all the butter is absorbed and the vegetables are evenly coated.
Whisk in Chicken Broth and Spices: Slowly whisk in the chicken broth, scraping the brown bits from the bottom. Add the red pepper flakes, thyme, salt, and pepper. Cook until the sauce thickens and the vegetables are tender.
Add Peas and Chicken: Mix in the peas and cook for a few minutes until they are warm. Then add the shredded chicken. Remove from heat. Pour the filling into a 9 x 13 pan.
Preheat Oven: Preheat the oven to 400℉
Assemble: Roll out the cheddar crust into a large rectangle on a lightly floured surface. Cover the filling with the crust. Brush with an egg wash (a lightly beaten egg mixed with a splash of water).
Bake: Bake the pot pie for 20-25 minutes, until the crust is golden brown and the filling is bubbling. Serve immediately.