Heat 1 tablespoon oil in a large nonstick skillet over medium-high heat. Add meatballs and turn to coat. Reduce heat to medium and cook, turning occasionally, until browned and cooked through, about 15 minutes. Transfer meatballs to a large saucepan and cover.

Wipe skillet clean; add remaining 2 tablespoons oil with the onion and cook over medium-high heat, stirring occasionally, until just softened, about 4 minutes. Add bell pepper; cook, stirring occasionally, until softened and just starting to brown, 6 to 8 minutes.

Heat broiler and place rack 6 inches from heat. Place rolls, cut side up, on a baking sheet. In saucepan with meatballs, add sauce and heat over medium heat until warm, about 2 minutes; spoon onto each roll. Cover with onion-bell pepper mixture and top each with 2 cheese halves. Broil until cheese is melted, 1 to 2 minutes.