Brush onion, bell pepper, and eggplant with 1 tablespoon oil.
Add onion and bell pepper to pan; cook 3 minutes on each side or until grill marks appear.
Remove from pan.
Add eggplant to pan; cook 3 minutes on each side or until grill marks appear.
Remove from pan; coarsely chop vegetables.
Combine vegetables, remaining 1 tablespoon oil, parsley, and salt; toss to combine.
Spread 1/4 cup hummus over each flatbread, leaving a 1/2-inch border around edges. Divide vegetables over each flatbread; top each serving with 2 tablespoons cheese.