Preheat your oven to 400°F (200°C) so it is hot and ready for baking.
Melt the butter in a large skillet over medium heat.
Sauté the vegetables by adding the diced onion, carrots, and celery to the skillet. Cook them until they soften and smell fragrant, which usually takes about 5 minutes.
Stir in the flour and cook the mixture for exactly 1 minute. This crucial step cooks out the raw flour taste and helps build a rich base for your gravy.
Build the sauce by gradually whisking in the chicken broth and whole milk. Keep whisking continuously until the mixture thickens into a smooth, creamy gravy.
Add the flavor and protein by folding in the diced chicken, salt, black pepper, and dried thyme. Stir everything gently to combine, then remove the skillet from the heat.
Prepare the bottom crust by unrolling one refrigerated pie crust and pressing it gently into the bottom of a 9-inch pie dish. Transfer your warm filling directly into the lined dish.
Seal the pie by placing the second pie crust over the filling. Crimp the top and bottom edges together tightly to seal the pastry and keep the gravy inside where it belongs.
Vent the crust by cutting a few small slits in the top pastry with a sharp knife. This allows steam to escape so your crust stays beautifully crisp.
Bake the pie at 400°F for 35 to 40 minutes, or until the crust turns a glorious golden brown.
Cool before serving. Allow the pie to rest and cool fully before slicing. We know it smells amazing, but giving it time to set ensures you get neat, clean slices instead of a runny filling.
Garnish with a sprinkle of fresh thyme just before bringing it to the table.