Heat the olive oil in a large skillet over medium heat. Add the onion and garlic and cook until softened, about 5 minutes.
Add the flour and thyme, and cook for 1 minute. Gradually add the chicken broth and bring to a boil.
Add the peas and carrots, turkey, salt, and pepper. Cook until the vegetables are tender, about 5 minutes. Stir in the half-and-half and cheese.
Transfer the mixture to a 9-inch pie plate. Unfold the puff pastry and place it over the pie plate. Trim the edges and flute. Brush the top of the pastry with the beaten egg and sprinkle with the breadcrumbs.
Bake until the top is golden brown and the filling is bubbly, about 30 minutes.
Let cool for 10 minutes before serving.
Interesting Facts
Turkey pot pie is an American classic.
The first pot pies were made in ancient Rome.
Puff pastry is a type of dough that is made from layers of butter and dough that puff up when cooked.