Heat a large skillet over medium heat and cook the ground beef, chopped onion, sliced mushrooms, and optional green bell pepper, stirring and breaking the meat into crumbles until it is no longer pink, then drain off any excess fat.
Stir the pizza sauce and dried basil into the skillet mixture until thoroughly combined.
Transfer the beef mixture into a lightly greased 13×9-inch (3-quart) baking dish, spreading it into an even layer.
Sprinkle the shredded mozzarella over the beef base, then arrange the frozen tater tots in a single layer on top.
Bake uncovered at 400°F for 30 to 35 minutes, or until the tater tots are lightly browned and crisp.
Remove the casserole from the oven, evenly scatter the cheddar cheese over the top, and return to the oven for about 5 minutes, or until the cheddar is fully melted.