Sauté the Vegetables: In a large skillet or saucepan, melt the butter over medium heat. Add the diced onion, carrots, and celery. Cook for about 5 minutes until softened, then add the garlic and cook for another 1-2 minutes until fragrant.
Create the Sauce: Sprinkle the flour over the sautéed vegetables and stir to coat evenly. Cook for 1-2 minutes, allowing the flour to absorb the butter and create a roux. Slowly add the chicken broth, stirring continuously to avoid lumps, then add the milk or heavy cream.
Add Chicken and Seasonings: Add the shredded chicken, frozen peas, frozen corn, thyme, rosemary, salt, and pepper. Stir to combine, then remove from heat.
Prepare the Biscuit Dough : In a large mixing bowl, whisk together the flour, baking powder, baking soda, garlic powder, salt, and paprika (if using). Add the cubed cold butter, cutting it into the flour mixture with a pastry cutter or your fingers until it resembles coarse crumbs. Do not overmix.
Top the Filling: Drop spoonfuls of the biscuit dough over the chicken pot pie filling in the baking dish, covering the surface but leaving some gaps for steam to escape.
Bake: Preheat your oven to 400°F (200°C). Set the baking dish in the oven and allow it to bake for 25 to 30 minutes, or until the biscuits are a rich golden brown and the filling is bubbling enticingly.
Add the Garlic Butter Topping: While the pot pie is baking, melt the butter and mix it with garlic powder and fresh parsley. Once the pot pie is done, brush the garlic butter over the tops of the biscuits.
Present: Let the dish rest for a few moments to cool slightly before serving. Enjoy this comforting chicken pot pie with a side salad or on its own for a delicious, hearty meal.