In a large skillet over med-high heat, melt butter with olive oil.
Add carrots and onions. Sauté until onions are translucent.
Add minced garlic and shredded turkey, sauté another minute until garlic is fragrant.
Sprinkle the flour on top and stir together. Cook 2-3 minutes, stirring often.
Slowly add chicken broth while constantly stirring.
Bring to a boil and boil 1-2 minutes until thickened, then reduce heat to low.
Stir in heavy cream and simmer until thickened. Remove from heat.
Stir in frozen peas.
Pour filling into a deep 9x13 casserole dish.
Drop mashed potatoes by tablespoons and spread out with fingers to mostly cover the mix.
Evenly add crumbled stuffing over the mashed potatoes.
Roll pie crust out to about 10x14 inches.
Top the filling with the pie crust.
Beat the egg and water together to create an egg wash and brush an even layer over crust.
Using a pairing knife, make 6-7 slits to vent the steam.
Bake at 375°F for 45-50 minutes or until the crust is a deep golden brown and the filling is bubbly.