Heat the oven to 375℉ and defrost your puff pastry if it has been frozen.
½ pound puff pastry
If you are using leftover turkey, pull the turkey off any bones and chop or pull the cooked turkey into bite-sized pieces.
2 cups cooked turkey
Heat the oil or butter in a large pot and then cook the chopped onions until they are soft and just starting to brown.
2 tablespoons butter or olive oil, 1 medium onion
Add the chopped carrot, celery, and potatoes. Stir and cook for a minute or two. Then add the minced garlic, salt, pepper, and herbs, and stir for a minute.
2 medium carrots, 2 stalks celery, 2 Yukon gold potatoes, 2 cloves garlic, 1 teaspoon salt, 1 teaspoon dried thyme, 1 teaspoon dried tarragon, ½ teaspoon ground black pepper
Add the flour and stir constantly to coat all of the vegetables and prevent the flour from burning.
½ cup (65 grams) all purpose flour
Add the chicken broth and vermouth or white wine. Bring to a boil, then turn down the heat until the liquid is at a simmer and cook until it thickens, stirring occasionally. This should take 5 to 10 minutes or so.
4 cups (32 ounces) chicken broth, ¼ cup vermouth or white wine
Add the chopped turkey and the peas, and let the filling cool.
¼ cup peas
Dust your countertop lightly with flour, and roll out your puff pastry to about a quarter inch thick. Be careful not to roll over the edge of the dough,which would compress the puff pastry layers together. Roll out or cut your puff pastry into a circle just slightly larger than your pie pan or ramekins. Divide the pot pie filling into four large individual ramekins, a 9 inch pie plate, or another serving dish able to accommodate all of the filling.
Top the turkey pot pie or pies with the puff pastry circle and use a sharp knife to cut a vent in the top. Brush with a slightly beaten egg.
1 large egg
Bake until the puff pastry turkey pie is a golden brown and the filling is bubbling, about 30 to 40 minutes. Baking the pot pies on top of an old baking sheet can help with clean up if the filling overflows.