Make the Filling: While the dough is chilling, prepare the filling. In a large pan, heat the 2 tablespoons of oil over medium heat. Add the chopped onion and sauté for 5-6 minutes, or until the onion becomes soft and translucent. This helps release the natural sweetness and aroma of the onion, which will add depth to the filling.
Cook the Carrots: Add the diced carrots to the pan and cook for 3-4 minutes, allowing them to soften slightly but still maintain some texture. The carrots add both flavor and color to the filling.
Cook the Ground Beef: Add the ground beef to the pan, breaking it apart as it cooks. Stir occasionally for 4-5 minutes, or until the beef is browned and fully cooked. Season the meat with salt, pepper, and thyme for flavor. The thyme adds a savory herbal note that complements the beef and vegetables.
Thicken the Filling: Sprinkle the flour over the meat mixture and stir to combine. The flour will help thicken the filling as it cooks. Gradually add the water or beef broth to the pan, stirring constantly to avoid lumps. Cook for another few minutes until the mixture has thickened to your liking. Once thickened, remove the pan from the heat and set it aside to cool.
Roll Out the Dough: Once the dough has chilled, divide it into 4 equal pieces. On a lightly floured surface, roll each piece of dough to about 1/8-inch thickness. Use a round cutter, a glass, or a bowl to cut out circles of dough that are large enough to encase the filling. You can adjust the size depending on how large or small you want your meat pies to be.
