Leftover Thanksgiving Turkey Pot Pie

Ingredients

• 3 tablespoons unsalted butter
• 12 ounces boneless, skinless cooked turkey, shredded or diced (about 3 cups)
• 1/2 medium yellow onion, diced (about 3/4 cup)
• 2 small or 1 1/2 medium carrots, peeled and thinly sliced crosswise (about 3/4 cup)
• 2 small or 1 1/2 medium stalks celery, thinly sliced crosswise (about 3/4 cup)
• 1 1/2 teaspoons fresh thyme leaves, or 3/4 teaspoon dried thyme
• 1/4 cup plus 2 tablespoons all-purpose flour
• 1 1/2 cups low-sodium turkey or chicken broth
• 1 cup plus 2 tablespoons whole or 2 percent milk, plus more for brushing
• 1 teaspoon kosher salt, plus more as needed
• 1/4 teaspoon freshly ground black pepper, plus more as needed
• 1/2 cup frozen peas
• 1 store-bought or homemade pie crust, thawed if frozen