Melt butter in a saucepan over medium heat. Add onions and cook onions for a few minutes until soft. Add garlic and cook 1 minute more.
Whisk in flour to form a thick paste. Add chicken stock gradually while whisking, followed by milk or half and half. Season with salt and pepper.
Add potatoes and carrots and bring to a boil, stirring often. Then add green beans, peas, chicken, and herbs. Taste and adjust seasoning as needed.
Carefully dump mixture into 9×2-inch pie dish. (If you’re using a smaller pie dish, you’ll have some leftover filling).
Roll out pie crust to a rough 10 or 11-inch circle then transfer to the top of your pie dish. Fold edges over and crimp if desired. Brush with an egg wash of whisked egg and water, and cut slits into the top for vents.
Place prepared pot pie on a sheet pan to catch any drips and bake at 400°F for 45-55 minutes until crust is golden and filling is bubbling on the sides or through the vents.
Let rest for about 10-15 minutes, then serve.
Note: Chicken pot pie is a great make-ahead dish. You can freeze it baked and unbaked. Bake as directed from frozen, adding a few minutes to baking time, or warm a baked frozen pie in a 350°F oven for about 30 minutes. Baked chicken pot pie also can be stored in the fridge for up to 5 days and warmed in the oven the same way.
Calories: 242kcal, Carbohydrates: 18g, Protein: 12g, Fat: 13g, Saturated Fat: 5g, Trans Fat: 1g, Cholesterol: 40mg, Sodium: 498mg, Potassium: 228mg, Fiber: 1g, Sugar: 3g, Vitamin A: 1591IU, Vitamin C: 4mg, Calcium: 39mg, Iron: 1mg