01 - Preheat oven to 400°F.
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. Cook, breaking up the meat, until browned, about 5-6 minutes.
04 - Stir in tomato paste, Worcestershire sauce, thyme, and rosemary. Cook for 1 minute to blend flavors.
05 - Sprinkle flour over the mixture; stir well to coat. Pour in beef broth, bring to a simmer, and cook until thickened, about 5 minutes.
06 - Add peas, season with salt and pepper, and cook for an additional 2 minutes. Remove from heat and let filling cool to room temperature.
07 - Roll out puff pastry sheets and cut into 6 circles about 4.5 inches in diameter for bases, and 6 slightly smaller circles for tops.
08 - Place pastry bases into a greased muffin tin or individual pie tins, pressing gently to fit.
09 - Divide the cooled beef filling evenly among the pastry bases.
10 - Brush edges of pastry with beaten egg. Place pastry tops over filling and seal by pressing edges with a fork. Cut a small steam vent in each pie top.
11 - Brush tops with remaining egg wash for golden color.
12 - Bake for 20-25 minutes, or until pastry is golden and crisp.
13 - Cool slightly before removing from tins and serving.