Step 1: Prepare the Filling

1. Preheat your oven to 375°F (190°C).
2. Heat butter in a large skillet over medium heat. Add the chopped onion and cook for about 3-4 minutes, until softened.
3. Add the minced garlic and cook for another 30 seconds until fragrant.
4. Stir in the shredded chicken and cook for 5-6 minutes until lightly browned.
5. Sprinkle the flour over the chicken and stir well to coat.
6. Slowly pour in the chicken broth, stirring continuously until the mixture begins to thicken, about 3-4 minutes.
7. Stir in the heavy cream and frozen peas. Simmer for 5 minutes until the filling becomes creamy.
8. Add the fresh thyme, parsley, salt, and pepper to taste. Remove from heat and let it cool slightly.

Step 2: Prepare the Puff Pastry

1. Lightly grease a muffin tin and preheat your oven to 375°F (190°C).
2. Roll out the thawed puff pastry and cut it into squares (about 4-5 inches each) to fit into the muffin tin.
3. Gently press each square into the muffin tin, allowing the corners to hang over the edges.

Step 3: Assemble the Mini Pies

1. Fill each pastry shell with the prepared chicken mixture, filling them about three-quarters full.
2. Place another square of puff pastry over each filled cup.
3. Press the edges together and use a fork to crimp the edges for a decorative finish and to seal the pies.
4. Brush the tops with a beaten egg for a golden, glossy finish.

Step 4: Bake the Mini Pies

1. Place the muffin tin in the preheated oven and bake for 20-25 minutes, or until the puff pastry is golden brown and flaky.
2. Remove from the oven and allow the pies to cool for a few minutes before serving.