Start by cooking your veggies... the carrots, peas (or broccoli in our case) and potatoes. We just combine everything in a large pot of water and boil until everything is just tender, about 4-6 minutes. Then set them aside.

In a large pot or Dutch oven, melt the butter over medium heat. Once melted, add the onion and cook until translucent, about 3-4 minutes. Add the garlic and cook a minute or so more, until fragrant.

Increase the heat to med-high and sprinkle the flour over the onion. Stir to incorporate and cook while stirring for a minute or two. Then, whisking continually, slowly add in the chicken broth and the cream. Stir in all the seasoning and whatever else you'd like and let it come to a low boil.

Preheat the oven to 375°F. Lay the first pie dough disc into the bottom of a 9" pie dish. Pour the filling over the top. Lay the second dough disc over the top and trim any overhanging dough from around the edges. Use a fork or your fingers to crimp the edges and seal it.

Use a small, sharp knife to cut a few slits across the top, so the steam can vent. Use a pastry brush to brush the beaten egg all over the top crust. Bake for 35-45 minutes, or until the crust is golden brown. Use a pie shield if you'd like to prevent the edges of the crust from browning too much too quickly. I put it on before putting the pie in the oven and take it off with about 10 or so minutes left of bake time.