Cook macaroni in large pot of boiling water. Stir in broccoli 2 minutes before end of cooking.
Meanwhile, heat oil in large, deep, nonstick skillet over medium-high heat. Add onion and ham; cook, stirring, until onion has softened, about 2 minutes. Add garlic; season with salt and pepper.
Drain pasta and broccoli, reserving 1/4 cup water; toss in bowl with ham mixture and Cheddar. Add 3 tablespoons water, more if needed.
