Creating these Mini Chicken Pot Pies Muffins is simple and enjoyable if you follow these steps:

1. Preheat the Oven: Preheat your oven to 375°F (190°C) and grease a muffin tin.
2. Cook the Vegetables: In a skillet, melt butter over medium heat. Add the diced onions and mixed vegetables; cook for 5-7 minutes until softened.
3. Make the Filling: Add the flour to the skillet and stir for 1 minute. Gradually pour in the chicken broth while stirring. Add milk and season with garlic powder, thyme, salt, and pepper. Cook until the mixture thickens, then remove from heat.
4. Add Chicken: Fold in the shredded chicken into the filling mixture until well combined.
5. Prepare the Dough: Open the refrigerated biscuit dough and cut each biscuit into quarters.
6. Assemble the Muffins: Place pieces of the dough into each muffin cup, pressing down to create a base. Spoon the chicken filling into each cup, filling them about ¾ full.
7. Top with Dough: Use remaining biscuit pieces to cover the tops of the filling, ensuring to pinch the edges to seal.
8. Egg Wash: Brush the tops of the muffins with the beaten egg for a golden finish.
9. Bake: Bake in the preheated oven for about 20-25 minutes or until muffins are golden brown.
10. Cool: Remove from the oven and allow the muffins to cool in the pan for 5-10 minutes before transferring to a wire rack.

Following these steps will yield delightful Mini Chicken Pot Pies Muffins that are bursting with flavor!