Preheat the oven to 350°F
In a large skillet over medium heated melt the butter. When the butter is gently sizzling, add the mushrooms, onions, and bell peppers; cook for a few minutes until the veggies are softened, 8-10 minutes.
Sprinkle the flour over the vegetables in the skillet; cook for 1 minute, stirring often.
Remove the skillet from the heat and gradually stir in the milk. When the milk has incorporated into the flour a bit, return the skillet to the burner.
Cook the sauce for 2-3 minutes, stirring, until nicely thickened; season to taste with salt and pepper.
Into a greased 11x8 baking dish, add the shredded chicken and potatoes; pour the sauce and mushroom mixture over the top, then sprinkle with cheese.
Bake on the center oven rack for 30-35 minutes or until hot and bubbly throughout and 160 degrees F. at the center.
Let the casserole rest for 5 minutes before serving.
