Preheat the oven to 375°F, and lightly grease a 2.5-quart baking dish. Set aside.
In a large skillet over medium heat, melt the butter. Add the onion and mixed vegetables. Cook until they begin to soften.
3 tablespoons unsalted butter, 1 cup diced white onion, 3 cups frozen mixed vegetables
Add the garlic and thyme. Stir for about 30 seconds, then sprinkle in the flour. Cook the flour for 2 to 3 minutes.
1 tablespoon minced garlic, 1 teaspoon dried thyme, ⅓ cup all-purpose flour
Slowly whisk in the chicken broth and milk. Let the sauce thicken, then taste and season with salt and pepper.
1 ½ cups low-sodium chicken broth, 1 cup whole milk, Salt, Black pepper
Stir in the turkey. The filling should be creamy. Transfer it to the prepared baking dish or leave it in an oven-safe skillet.
3 cups cooked turkey
Place the puff pastry on a lightly floured surface. Roll it just enough to smooth the creases.
1 sheet puff pastry
Lay the sheet over the dish or cut it into small squares for a patchwork topping. Cut several small slits in the top if using a full sheet.
Whisk the egg and water. Brush it over the pastry.
1 large egg, 1 tablespoon water
Bake for 35 to 45 minutes, or until the pastry is puffed and golden brown.
Let the pot pie rest for 5 to 10 minutes before serving.