Preheat the oven to 400°F. In a large skillet, melt butter over medium heat. Add cooked chicken and frozen vegetables; cook until heated through, about 5 minutes.
Stir in flour until well combined. Gradually whisk in chicken broth and heavy cream; cook until thickened, about 5-7 minutes. Season with salt and pepper. Remove from heat and stir in shredded cheese.
Pour filling into a pie dish. Cover with puff pastry or pie crust, sealing edges. Cut a few slits in the top for steam to escape.
Bake in the preheated oven until the crust is golden brown, about 25-30 minutes. Let cool slightly before serving.
Notes
This chicken pot pie is perfect for a cozy dinner. You can add carrots or peas for extra veggies.