Add the oil to a large pot over high heat. Once the oil begins to shimmer, add the chicken, and stir until cooked through, about 7 minutes. Transfer the chicken to a bowl.
3. Step
Melt butter in the same pot. Add the onions and carrots and stir until softened, about 8 minutes.
4. Step
Add the flour, stirring to combine. Slowly add the milk and chicken broth, alternating between the two, stirring continuously and bringing to a boil.
5. Step
Add the cooked chicken, peas, salt, and pepper, and stir until thoroughly mixed. Remove from heat and let cool.
6. Step
Lay out puff pastry sheets and use a small 6-inch (15 cm) bowl to cut circles out of it.
7. Step
Place dough circles in a nonstick muffin tin and fill with pot pie mixture.
8. Step
Using remaining puff pastry, cut ⅛-inch (3 mm) strips of dough, and make a lattice top for each muffin cup. Brush the lattice tops with the egg.
