Preheat oven to 400 degrees F.
Over medium heat in a large skillet add the butter, carrots, celery, onions, and potatoes sautee until the vegetables begin to soften about 7 to 10 minutes.
Add the flour and stir in until the flour is combined.
Turn the heat to medium-high and slowly add the milk and the broth stirring continuously. Cook until the liquid starts to thicken.
Add the chicken and the peas and stir in. Pour the filling into a 9 by 13-inch baking dish.
Arrange the tater tots over top of the filling.
Place the casserole in the preheated oven. Bake 30 to 40 minutes or until the tater tots are browned.
Remove from the oven and serve