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Step 1
Stovetop: Place the chicken and 2 cups broth in a large pot or Dutch oven and bring it to a simmer over medium heat. Cook the chicken until it is just done (don’t overcook or it will dry out) – about 10-12 minutes. If the chicken pieces are large, you may need to pound them or cut them in half so they will cook more quickly.
Step 2
Slow Cooker: Or you can place the chicken and broth in a slow cooker and cook on high for 3 hours or low for 5 hours.
Step 3
Transfer the cooked chicken to a medium bowl. Pour the broth through a fine-mesh strainer into a liquid measuring cup and reserve. Return the pot to the stovetop (no need to wash it).
Step 4
Heat the olive oil in the now-empty pot over medium heat. Add onion, carrots, and celery, and peas. Add salt and pepper to taste, if desired. Cover and cook, stirring occasionally, until just tender, about 5 minutes. While the vegetables are cooking, shred or chop the chicken into small bite-size pieces. Transfer the cooked vegetables to the bowl with the chicken; set aside.
Step 5
Over medium heat, melt the 4 Tbsp butter in the empty pot. Stir in the flour and cook for one minute, stirring constantly. Slowly whisk in the reserved chicken broth and milk. Bring to a simmer and stir occasionally until the sauce thickens, about 5 minutes, taking care not to burn the bottom. Add 1/2 tsp salt and 1/2 tsp pepper.
Step 6
Remove from the heat and stir the chicken, vegetables and peas into the sauce. Transfer to medium bowl, cover with plastic wrap and refrigerate until chilled, about an hour (only if freezing the pies and not cooking immediately).
Step 7
Unwrap and unroll pie crusts onto lightly floured surface. Cut out 2-3 pastry toppings by cutting around the edge of an overturned pan.
Step 8
Divide mixture among the number of disposable aluminum loaf pans you have. Top with pastry and use fork to seal edges.
Step 9
Using a paring knife, make 3 steam vents in each crust.
Step 10
Tightly wrap each loaf pan in 2 layers of plastic wrap and 1 layer of foil. Freeze for up to 2 months.
Step 11
Adjust oven rack to middle position and heat oven to Unwrap frozen pot pies and arrange on a rimmed baking sheet. Brush crust with beaten egg, cover with foil, and bake 40 minutes. Uncover and bake until crusts are golden brown, about 20 minutes. Let pot pies rest 10 minutes before serving.