01 - Preheat your oven to 400°F.
02 - Heat olive oil in a large skillet over medium heat. Add the onion and carrot; sauté for 3–4 minutes until softened.
03 - Add the 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 meld flavors.
05 - Sprinkle flour over the mixture; stir well to coat. Pour in the beef broth, bring to a simmer, and cook until thickened, about 5 minutes.
06 - Add the peas, season with salt and pepper, and cook for an additional 2 minutes. Remove from heat and let the filling cool to room temperature.
07 - Roll out the puff pastry sheets and cut into 6 circles, about 4.5 inches in diameter, for the bases, and 6 slightly smaller circles for the 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 the pastry with beaten egg. Place the pastry tops over the 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 a golden finish.
12 - Bake for 20–25 minutes, or until pastry is golden and crisp.
13 - Cool slightly before removing from the tins and serving.