Preheat your oven to 400°F (200°C) and lightly grease a muffin tin.
In a large skillet, heat the olive oil over medium heat. Add the diced onion and minced garlic, sautéing until softened, about 3-4 minutes.
Stir in the shredded chicken and frozen mixed vegetables, cooking for an additional 2-3 minutes until warmed through.
Pour in the chicken broth and heavy cream, then add the thyme, rosemary, salt, and pepper. Bring to a simmer and let cook for 5-7 minutes, stirring occasionally, until the mixture thickens slightly.
Roll out the puff pastry on a lightly floured surface and cut into circles that are about 5 inches in diameter.
Press the pastry circles into the muffin tin cups, ensuring that there is extra hanging over the edges.
Spoon the chicken mixture into each pastry-lined muffin cup, filling them generously.
Use any excess pastry to create tops for your mini pot pies, either by cutting more circles or creating lattice patterns. Press edges to seal.
Beat the egg in a small bowl and brush the tops of the pies with the egg wash for a golden finish.
Bake in the preheated oven for 20-25 minutes or until the pastries are golden brown and puffed.
Allow the mini pot pies to cool for a few minutes before carefully removing them from the muffin tin.
Notes
Serve warm, garnished with fresh herbs for added flavor.