Prepare the Filling: Melt the butter in a sauté pan over medium heat. Add the chopped onions and garlic, and cook until soft, 3 to 4 minutes. Add the diced carrots and potatoes and stir to combine, cooking for another 5 minutes, stirring occasionally.
Make the Gravy: Add the flour and stir to combine. Cook for one to two minutes to eliminate any raw flour taste. Slowly incorporate the beef broth for a lump-free meat mixture, whisking continuously. Bring the mixture to a simmer and cook for 5-7 minutes until it thickens.
Combine Ingredients: When the gravy is thickened, stir in the shredded beef, the peas, the Worcestershire sauce, thyme, heavy cream and salt and pepper to taste. Cook for an additional 3 minutes until the meat is warmed through. Please take off the heat and let it cool a little.
Assemble the Pie: Heat your oven to 375°F (190°C). Roll out the pie crust to line your baking dish. Pour the beef and vegetable mixture into the prepared dish and spread it into an even layer. Cover the pie with the rolled-out pie crust, pressing down the edges to seal. Cut a few small slits in the top to allow steam to escape during baking.
Bake: For a golden, glossy finish, brush the top of the crust with melted butter or an egg wash. Put in the oven and bake for 45-50 minutes or until the crust is golden brown and the filling is bubbly.
Resting Time: Let the pie rest for 5 minutes, then slice and serve. It helps the filling set up and makes it easier to cut.