In a skillet, heat olive oil over medium heat. Add chopped onions and carrots; cook for about 5 minutes until softened.

Stir in minced garlic and cook for another minute until fragrant.

Add ground beef, break it apart, and cook until browned and no longer pink.

Stir in tomato paste and cook for 2 minutes.

Sprinkle flour over the mixture and stir to coat evenly.

Slowly pour in beef broth while stirring to avoid lumps.

Add thyme, parsley, salt, and pepper. Simmer for 5–7 minutes until thickened. Let the filling cool.

Preheat oven to 400°F (200°C). Roll out the dough and cut into 6-inch circles.

Place 2–3 tablespoons of filling on one side of each circle. Fold and seal the edges with a fork.

Place pies on a lined baking sheet and brush the tops with beaten egg.

Bake for 20–25 minutes or until golden brown and crispy.