Preheat the oven to 400° Fahrenheit (200° Celsius)
Cook the Vegetables:
Heat a cast iron pan (or any oven-safe pan) over medium heat and add 2 tablespoons of butter. Once melted, add the onion, celery, garlic, dried sage, ½ teaspoon of pepper, and ½ teaspoon of salt. Cook, stirring occasionally, until the vegetables are softened, about 3-5 minutes.
Sauté the Mushrooms and Carrots:
Add the mushrooms and carrots to the pan along with the remaining 1 tablespoon of butter, 3 sprigs of thyme, ½ teaspoon of pepper, and ½ teaspoon of salt. Cook until the mushrooms and carrots are tender, about 5 minutes.
Make the Sauce:
Sprinkle the flour over the mixture and stir until well incorporated.
Gradually pour in the chicken broth while stirring. Add the remaining 1 teaspoon of salt and 1 teaspoon of pepper. Continue to cook, stirring occasionally, until the mixture thickens, about 10 minutes.
Finish the Filling:
Remove the pan from heat. Stir in the heavy cream, turkey, peas, paprika, and adjust seasoning with additional salt and pepper if needed.
Prepare the Puff Pastry:
Unfold the puff pastry and place it over the filling in the pan. Trim any excess pastry if desired, or fold it over for a dramatic effect.
Add the Finishing Touches:
Using a sharp knife, make 3-4 slits in the center of the puff pastry. Whisk the egg with a small pinch of salt and brush it evenly over the puff pastry.
Bake and Cool:
Bake for 20 minutes, or until the top of the puff pastry is deep golden brown and the filling is bubbling. Allow to cool for 10 minutes before serving.
Notes
Thaw the Puff Pastry Properly - Puff pastry dough can be a bit tricky if it’s not handled right. Thaw it in the fridge overnight or on the counter for about 30 minutes. It should be cold but pliable. If it gets too warm, it can be hard to work with and may not puff up as nicely.Let the Pie Cool Before Serving - After baking, let the pot pie cool for about 10 minutes before serving. This allows the pot pie filling to set a bit, so it doesn’t spill out when you cut into it.Use a Casserole Dish - If you don't have an oven-safe pan, you can transfer the filling to a lightly greased casserole dish and put the puff pastry crust ontop!