Cook and stir beef, onion and garlic in 10-inch skillet over medium heat until beef is light brown; drain. Stir in tomatoes, jalapeņo pepper, salt and pepper; break up tomatoes with fork. Heat to boiling; reduce heat. Simmer uncovered until most of the liquid is evaporated, about 10 minutes.
Cut papayas lengthwise into halves; remove seeds. Place about 1/3 cup beef mixture in each papaya half; sprinkle with cheese. Arrange in shallow roasting pan. Pour very hot water into pan to within 1 inch of tops of papaya halves. Bake uncovered at 350 degrees F until papayas are very tender and hot, about 30 minutes.
