Preheat your oven to 400°F (200°C) so it is fully heated by the time your brisket pot pie is assembled.

Prepare the brisket by shredding or chopping 2 cups of cooked beef brisket into bite-sized pieces, removing any large pieces of fat.

Warm a large skillet or wide saucepan over medium heat and add 2 tablespoons of olive oil.

Add the finely chopped yellow onion to the skillet and cook for 3 to 4 minutes, stirring occasionally, until it softens and becomes translucent.

Stir in the diced carrots and diced celery, and cook for another 5 to 6 minutes until the vegetables begin to soften but are not completely tender.

Add the minced garlic to the vegetables and cook for about 30 seconds, just until fragrant, stirring constantly to prevent burning.

Add 2 tablespoons of unsalted butter to the skillet and let it melt completely, stirring it into the vegetables.

Sprinkle 3 tablespoons of all-purpose flour evenly over the vegetables and stir well to coat everything, cooking the flour for 1 to 2 minutes to remove the raw taste.

Slowly pour in 1.5 cups of beef broth while stirring continuously, breaking up any lumps so the mixture becomes smooth and begins to thicken.

Stir in 0.5 cup of whole milk or half-and-half, combining it with the broth mixture to create a creamy, velvety base for the pot pie filling.

Season the sauce by adding 1 teaspoon of Worcestershire sauce, 1 teaspoon of fresh thyme leaves (or 1/2 teaspoon dried thyme), 0.5 teaspoon of dried rosemary, 1 teaspoon of salt, and 0.5 teaspoon of black pepper, then stir well.

Add the shredded or chopped brisket to the skillet, stirring it into the sauce so the meat is evenly coated and begins to warm through.

Stir in 1 cup of frozen peas, mixing them into the filling until they are evenly distributed throughout the brisket and vegetables.

Let the filling simmer gently for 3 to 5 minutes, stirring occasionally, until it is thick, creamy, and bubbling; adjust salt and pepper to taste, then remove from heat.

Transfer the hot brisket pot pie filling into a 9-inch pie dish or similar oven-safe baking dish, spreading it out into an even layer.

On a lightly floured surface, gently roll out the thawed puff pastry sheet just enough to comfortably cover the top of your baking dish with a slight overhang.

Drape the puff pastry over the filled baking dish, tucking or crimping the edges along the rim to seal the pot pie and create a neat border.

Use a sharp knife to cut 4 to 5 small slits in the center of the puff pastry to allow steam to escape while baking.

Brush the top of the puff pastry evenly with the beaten egg wash, which will help the crust turn glossy and golden brown in the oven.

Place the brisket pot pie on a baking sheet to catch any drips, then bake in the preheated oven for 25 to 30 minutes, or until the puff pastry is deeply golden and the filling is bubbling around the edges.

Remove the pot pie from the oven and let it rest for 10 to 15 minutes so the filling can thicken slightly before serving.

Spoon the brisket pot pie into bowls or onto plates, making sure each serving has plenty of brisket, vegetables, gravy, and a generous piece of flaky puff pastry crust.