1. In 2-quart saucepan over medium heat, in hot salad oil, cook onion and green pepper until tender. Add tomatoes with their liquid, salt, basil, and sugar; over high heat, heat to boiling, stirring to break up tomatoes. Reduce heat to low; simmer, uncovered, 10 minutes.
2. Meanwhile, shape ground beef into two 3/4 inch-thick patties. Over medium-high heat, heat 10-inch skillet until very hot. Arrange pat ties in skillet; cook 4 minutes for rare or until of desired doneness, turning patties once.
3. Spoon off any fat from skillet. Add tomato sauce; over high heat, heat to boiling. Reduce heat to low; top patties with mozzarella cheese. Cover skillet and heat until cheese melts.