Step 1

Arrange a rack in the middle of the oven and heat to 375°F. Fold a 2-foot-long sheet of aluminum foil in half lengthwise, then fold it in half again. Place the sub rolls on 2/3 of a rimmed baking sheet and wrap the foil strip around them. This will keep the rolls from drying out while the meatballs heat through and give you room to roast the broccoli without dirtying another pan.

Step 2

Arrange the broccoli in a single layer on the remaining third of the pan. Add the sloppy Joe sauce directly to the bag of frozen meatballs and shake to coat. Divide the meatballs between the sub rolls, then scoop any excess sauce over the meatballs. Sprinkle the sandwiches with the cheese.

Step 3

Bake until bubbly and the meatballs are heated through, about 25 minutes.