Cook and stir beef, onion, and garlic in 1-inch skillet over medium heat until beef is light brown. Drain; stir in tomatoes, jalapeno pepper, salt and pepper. Break up tomatoes with fork. Heat to boiling. Reduce heat; simmer uncovered, until most of the liquid is evaporated, about 1 minutes.
Cut papayas lengthwise into halves and remove seeds. Place aobut 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 35 degrees until papayas are very tender and hot, about 3 minutes.
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