1. Preheat oven to 400°F (200°C) and grease a muffin tin or prepare ramekins

2. In a saucepan, melt butter over medium heat and sauté onion until translucent, then add garlic and cook 30 seconds

3. Sprinkle flour over the mixture and whisk constantly for 1 minute

4. Slowly whisk in chicken broth until smooth, then add cream of chicken soup or heavy cream and stir until thickened

5. Fold in shredded chicken, mixed vegetables, thyme, and season with salt and pepper

6. Spoon the filling into prepared cups, filling nearly to the top

7. Flatten each biscuit and place on top of each portion, tucking edges slightly

8. Brush biscuit tops with beaten egg for a golden finish

9. Bake for 15 to 18 minutes until biscuits are golden brown and filling is bubbly

10. Let pies rest for 5 minutes before removing from the tin and serving