In a large pot or dutch oven over medium heat, melt butter and saute sweet potato, onion, carrots, and celery, season with salt and pepper. Stir often until starting to soften, about 15 minutes.
Add garlic, Italian seasoning, peas, and flour and stir well to combine for another minute.
Add stock, milk, chicken and season with salt. Allow the filling to thicken over medium low heat, stirring occasionally about 15 to 20 more minutes.
Preheat oven to 375°.
When thickened, transfer filling into casserole pans, it will fill about 2 medium pans or 1 larger one, but you can put it in any sizes or shapes you have, just divide the crust accordingly.
Meanwhile, make the crust (can be made at anytime and stored in the fridge, the pot pie filling can also sit while you make it). In a large bowl combine flour and salt, then work in butter with a pastry cutter and add water a little at a time until it comes together to form a pie dough. Work quickly to keep dough cold, cut into 2 equal portions and roll out on a floured surface with a rolling pin. Top casserole pans with the crust, crimping the edges, and cut a few slits in the top to vent. Whisk one egg and brush onto the crusts (you won't need all of it).
At this point the pies can be baked 45-60 minutes to eat, or stored in the fridge for a day or 2, or covered, refrigerated first and then frozen for 3 to 6 months. If freezing, thaw in fridge a day or two before baking and bake uncovered at 375° for 45-60 minutes, top should be crusty and filling hot and bubbly. Let sit 10 minutes before serving.