Heat oil in a large nonstick skillet over medium-high heat until hot. Add shrimp; cook, stirring constantly, 3 minutes or until done. Divide shrimp evenly among 4 individual gratin dishes; set aside.
Return skillet to medium-high heat. Add green onions and garlic; cook, stirring constantly, 1 minute. Add tomatoes, oregano, basil, sugar, and red pepper; cook 3 minutes or until liquid almost evaporates. Spoon tomato mixture evenly over shrimp, and sprinkle with cheese.
Broil 5 minutes or until cheese softens. (Cheese will not melt.)