01 - Preheat your oven to 400°F for baking the pies.
02 - Heat olive oil in a large skillet over medium heat. Add onion and carrot; sauté for 3–4 minutes until softened.
03 - Add garlic and ground beef to the skillet. Cook, breaking up the meat with a spoon, until browned, approximately 5–6 minutes.
04 - Stir in tomato paste, Worcestershire sauce, dried thyme, and rosemary. Cook for 1 minute to meld flavors.
05 - Sprinkle flour over the mixture, stirring well to coat. Pour in beef broth, bring to a simmer, and cook until thickened, about 5 minutes.
06 - Add frozen peas to the skillet. Season with salt and black pepper to taste. Cook for an additional 2 minutes.
07 - Remove from heat and allow the filling to cool completely to room temperature before assembling pies.
08 - Roll out puff pastry sheets and cut into 6 circles approximately 4.5 inches in diameter for bases, and 6 slightly smaller circles for tops.
09 - Place pastry bases into a greased muffin tin or individual pie tins, pressing gently to fit the shape.
10 - Divide the cooled beef filling evenly among the pastry-lined tins.
11 - Brush pastry edges with beaten egg. Place pastry tops over filling and seal edges firmly by pressing with a fork.
12 - Cut a small steam vent in the top of each pie. Brush tops generously with remaining beaten egg.
13 - Bake for 20–25 minutes until pastry is golden brown and crisp.
14 - Cool slightly before removing from tins. Serve warm as a main dish.