01 - Preheat oven to 400°F. Lightly grease a standard 12-cup muffin tin to prevent sticking.
02 - Roll out pie crusts on a lightly floured surface. Cut out 12 rounds approximately 4 inches in diameter for the bases and 12 smaller rounds about 2.5 inches for the tops.
03 - Gently press the larger pastry rounds into the bottom and up the sides of each muffin cup, ensuring full coverage.
04 - In a skillet over medium heat, melt unsalted butter. Add chopped onion and sauté until translucent, approximately 3 minutes.
05 - Add flour to onions and stir, cooking for 1 minute to form a roux.
06 - Gradually whisk in chicken broth and whole milk. Stir continuously and cook until sauce thickens, about 3 minutes.
07 - Add diced turkey, thawed mixed vegetables, salt, pepper, and thyme to the sauce. Stir well and cook for an additional 2 minutes, then remove from heat.
08 - Evenly spoon turkey and vegetable mixture into each prepared pastry-lined muffin cup.
09 - Cover pies with smaller pastry rounds, pressing edges gently to seal. Cut a small slit in the top for steam to escape.
10 - Brush tops of each pie lightly with beaten egg for gloss and even browning.
11 - Place muffin tin in oven and bake for 20 to 25 minutes, or until crust is golden brown.
12 - Allow pies to cool in the tin for 5 minutes. Carefully remove and serve warm.