Preheat your oven to 425°F (220°C).
Place one of the pie crusts into a 9-inch pie plate, allowing it to slightly overhang at the edges.
In a skillet over medium heat, brown the ground beef until fully cooked. Add in the finely chopped onion, minced garlic, and diced carrots, cooking until they are soft and fragrant.
Sprinkle in the all-purpose flour and stir well to coat everything evenly. Gradually pour in beef broth and Worcestershire sauce while stirring continually until combined; let this mixture simmer for about five minutes before removing it from heat.
Pour the flavorful filling into your prepared crust, spreading it out evenly. Cover with the second crust, crimping edges together tightly; don't forget to cut slits on top for steam release and brush with beaten egg for that lovely shine.
Place your assembled pie into the preheated oven and bake for 30–35 minutes or until golden brown on top. If edges start browning too quickly, cover them with foil halfway through baking.