Step 1: Preheat oven to 400°F (200°C) and grease a mini muffin tin.
Step 2: In a large skillet, sauté onion, celery, and garlic over medium heat until softened, about 5 minutes.
Step 3: Stir in flour and cook for 1 minute, then gradually whisk in chicken broth until smooth.
Step 4: Add heavy cream, thyme, salt, and pepper, and simmer until thickened, about 5 minutes.
Step 5: Stir in shredded chicken and frozen vegetables, then remove from heat and let cool slightly.
Step 6: Roll out puff pastry and cut into 24 squares (about 2×2 inches each).
Step 7: Press each pastry square into a mini muffin tin cavity, then fill with chicken mixture.
Step 8: Brush edges of pastry with egg wash and fold corners to seal, creating a bite-sized pie.
Step 9: Bake for 15-20 minutes until golden brown and bubbling.
Step 10: Let cool for 5 minutes before serving warm.