- Preheat the oven to 350°F.
- In a heavy 10 to 12 inch skillet, heat the oil over moderate heat until a light haze forms above it.
- Sauté onions and garlic until they are soft and transparent but not brown.
- Stir in the beef breaking it up with a fork and cook until all traces of pink disappear.
- Add the tomatoes (or substitute 1½ cups chopped, drained canned tomatoes), chilies, salt and pepper.
- Stirring occasionally, cook briskly until most of the liquid in the pan has evaporated and the mixture is thick enough to hold its shape almost solidly in the spoon.
- Taste for seasoning.
- Spoon the meat mixture into the papaya shells, spreading and smoothing the filling with a spatula.
- Place the shells side by side in a shallow roasting pan.
- Pour enough boiling water in the pan to come about 1 inch up the sides of the papaya.
- Bake for 1 hour then sprinkle each shell with 1 tbsp of the cheese and bake for 30 minutes, or until the top is delicately browned.
- Top shells with remaining cheese when ready to serve.