Heat gas or charcoal grill to high heat, about 400 degrees. Cut 4 (12x12-incsheets of heavy-duty foil.
Fill each foil pack with 2 cups of broccoli and 1 cup of chopped sausage. Add salt and pepper to taste.
Bring up 2 sides of foil so edges meet. Seal edges, making tight 1/2-inch fold; fold again, allowing space for heat circulation and expansion.
Place packs on the grill, cook for 7 minutes. Flip foil packs and cook for 7 more minutes.
Carefully open packs and sprinkle each pack with 114 cup of shredded cheddar cheese. Using tongs, tent the foil pack over the foil pack allowing the cheese to melt. Cook 2-3 more minutes and remove from heat.