Bring a medium size pot of water to a boil. Add the chicken breast and cover with a lid. Turn down the heat to medium. Cook for 15 minutes. Remove the pot from heat source and let chicken rest in the pot for 10 minutes. Remove the chicken then shred and set aside. OR use 3 cups of precooked/shredded chicken.
Heat a separate sauce pan to medium-high. Melt the butter. Then sauté the onion, celery, and carrots for 4-5 minutes or until fragrant. Lastly, add garlic and cook for an additional 30 seconds or until fragrant.
Add flour and mix until ingredients are well coated. Pour half of the broth in the pan and mix. Then pour the rest of the broth while continuing to mix everything together.
Turn the heat down to medium. Add salt, pepper and heavy whipping cream. Then continue to mix everything together. Add cooked chicken, continuing to mix. Add frozen peas and mix. Cook for 7-10 minutes or until it thickens. Season with salt & pepper to taste. Remove from the heat. Let cool for 15 minutes.
Preheat the oven to 375°F.
Pie Crust: homemade or store bought (follow the instructions on the box as directed). In a 9" pie pan: roll out the crust, place it in the pan. Gently press the crust against the pan (bottom and sides).
Add filling in to the pan. Top with the second pie crust. Tuck the top of the crust underneath the crust edges (see video for reference). Then, flute or crimp the crust. If needed; gently press down on the crust to level the pie.
Egg wash: in a small bowl, add the egg and water. Whisk until well combined. Brush the egg wash over the surface of the pie crust. Cut 5-6 slits on top of the pie shell. Sprinkle with kosher salt.
Bake at 375°F for 45 minutes or until golden brown. After 20 minutes, cover the edges of the crust with aluminum foil (to prevent burning). Tip: fold the rectangular foil in half, cut a semicircle out of the the middle. Unfold the foil and you should have circular opening in the foil just big enough to cover the pie edges.
Remove from the oven. Discard the foil. Let rest for 10 minutes before serving.