Heat the butter and olive oil in a large skillet over medium heat. Add the onion, carrots, and celery. Cook 5 to 7 minutes, until softened.
Add the Turkey and Vegetables
Stir in the turkey, corn, peas, smoked paprika, thyme, and rosemary. Season with salt and pepper.
Thicken the Filling
Sprinkle the flour over the mixture and stir for 1 minute.
Slowly pour in the stock while stirring. Bring to a gentle simmer.
Add the cream and cook 3 to 4 minutes, until thickened.
Assemble the Pot Pie
Put the hot filling in a 9-inch pie dish (or 4 to 6 ramekins for minis).
Lay the puff pastry over the top and trim the excess.
Cut 3 to 4 small slits to vent. Brush with the egg wash.
Bake
Bake at 400°F (204°C) for 25 to 30 minutes, until the top is puffed and deep golden brown.
Cool and Serve
Let it cool 10 minutes so the filling settles. Serve warm.
Notes
Use thawed supermarket frozen puff pastry and keep it cold until you top the pie. Set the dish on a sheet pan to catch drips. You can assemble it ahead and freeze it baked or unbaked. See the freezing box for reheating and baking times.