Follow these steps carefully for perfectly baked mini chicken pot pies:

Part 1: Prepare the Pie Crust (if making from scratch)

1. Combine Dry Ingredients: In a large bowl, whisk together the 2 ½ cups of all-purpose flour and 1 teaspoon of salt.
2. Cut in the Butter: Add the cold, cubed butter to the flour mixture. Using a pastry blender, your fingertips, or a food processor (on pulse), cut the butter into the flour until the mixture resembles coarse crumbs with some pea-sized pieces of butter remaining. This is key for a flaky crust.
3. Add Ice Water: Gradually sprinkle the ½ cup of ice water over the mixture, one tablespoon at a time, mixing lightly with a fork or your hands after each addition, just until the dough starts to come together. Be careful not to overmix. If the dough seems too dry, add a little more ice water, a teaspoon at a time.
4. Form and Chill Dough: Divide the dough in half, flatten each half into a disc, wrap tightly in plastic wrap, and refrigerate for at least 1 hour (or up to 2 days). Chilling allows the gluten to relax and the fat to solidify, resulting in a more tender and flaky crust.

Part 2: Prepare the Chicken Pot Pie Filling

1. Sauté Aromatics: In a large skillet or Dutch oven, melt the 2 tablespoons of unsalted butter over medium heat. Add the chopped onion, diced carrots, and diced celery. Sauté for 7-10 minutes, stirring occasionally, until the vegetables are softened but not browned. This step builds the flavor base.
2. Make the Roux: Sprinkle the ½ cup of all-purpose flour over the sautéed vegetables. Cook, stirring constantly, for 1-2 minutes. This cooks out the raw flour taste and creates the roux, which will thicken the sauce.
3. Create the Sauce: Gradually whisk in the 2 ½ cups of chicken broth, ensuring there are no lumps. Bring the mixture to a simmer, stirring frequently. The sauce will begin to thicken.
4. Add Creaminess and Seasonings: Stir in the ½ cup of heavy cream (or whole milk), dried thyme, and dried rosemary. Continue to simmer gently for another 3-5 minutes, or until the sauce has thickened to a gravy-like consistency.
5. Incorporate Chicken and Vegetables: Remove the skillet from the heat. Stir in the 2 cups of cooked chicken, 1 cup of frozen peas, and ½ cup of frozen corn (if using). Season generously with salt and freshly ground black pepper to taste. Mix well to ensure everything is evenly coated in the creamy sauce. Set aside to cool slightly while you prepare the crust for the muffin tins.

Part 3: Assemble and Bake the Mini Chicken Pot Pies

1. Preheat Oven and Prepare Muffin Tin: Preheat your oven to 400°F (200°C). Lightly grease a standard 12-cup muffin tin, or use non-stick cooking spray.
2. Roll Out Dough: On a lightly floured surface, take one disc of chilled pie dough. Roll it out to about ⅛-inch thickness.
3. Cut Crusts for Bottoms: Using a round cookie cutter or the rim of a glass that is slightly larger than the diameter of your muffin cups (typically 3.5 to 4 inches), cut out 12 circles for the bottoms of the pies. Gently press these dough circles into the greased muffin cups, ensuring they come up the sides.
4. Fill the Pies: Divide the prepared chicken pot pie filling evenly among the 12 dough-lined muffin cups. Fill them generously, as the filling won’t expand much.
5. Cut Crusts for Tops: Roll out the second disc of pie dough. Using a slightly smaller cookie cutter (around 2.5 to 3 inches) or a knife, cut out 12 circles or decorative shapes for the tops. If using solid circles, make sure to cut a few small slits in each top crust to allow steam to escape during baking. This prevents the filling from bubbling out excessively.
6. Place Top Crusts: Gently place the top crusts over the filling in each muffin cup. You can crimp the edges with a fork to seal them to the bottom crust if desired, or simply lay them on top.
7. Egg Wash: In a small bowl, beat the egg with a tablespoon of water to create an egg wash. Lightly brush the tops of the mini pies with the egg wash. This will give them a beautiful golden color and a slight shine.
8. Bake: Place the muffin tin on a baking sheet (to catch any potential drips) and bake in the preheated oven for 25-30 minutes, or until the crusts are golden brown and the filling is bubbly.
9. Cool Slightly: Once baked, remove the muffin tin from the oven and let the mini chicken pot pies cool in the tin for at least 10-15 minutes before carefully removing them. This allows the filling to set slightly and makes them easier to handle. You may need to run a thin knife around the edges to help release them.