Put the eggplant and papaya in a stock pan, cover with water and add a pinch of salt. Bring to a boil and simmer until the vegetables are soft, about 30-35 minutes.
Strain the vegetables and mash with a fork. Meanwhile, preheat the oven to 400F (200C). Heat the oil in a frying pan over medium heat and fry the onions until translucent. Add the garlic and mashed vegetables. Season to taste and add a sprinkle of red pepper flakes, if you like some spice.
Divide the vegetable puree over one big or a few small oven-proof bowls. Sprinkle with cheese and bake in the oven until the cheese is melted and browned, about 15 minutes. Serve immediately.