In a large skillet over medium heat, melt the butter. Add the diced onion, carrots, and celery. Cook for 5-7 minutes until vegetables begin to soften. Add the minced garlic and cook for another minute until fragrant.

Add the ground beef to the skillet, breaking it up with a spoon. Cook until browned, about 5-6 minutes. Drain any excess fat if necessary.

Sprinkle the flour over the beef mixture and stir to combine. Cook for 1 minute to remove the raw flour taste. Gradually pour in the beef broth while stirring constantly. Add Worcestershire sauce, thyme, salt, and pepper. Bring to a simmer and cook until thickened, about 3-4 minutes.

Stir in the frozen peas and remove from heat. Let the filling cool slightly while you prepare the pastry.

Preheat your oven to 400°F (200°C). Roll out the puff pastry sheets and cut circles slightly larger than your ramekins or individual pie dishes. Spoon the beef filling into 4-6 individual oven-safe dishes. Top each with a pastry circle, pressing the edges to seal. Brush with beaten egg and cut a small slit in the center for steam to escape.

Bake for 20-25 minutes until the pastry is golden brown and puffed. Let cool for 5 minutes before serving.