Peel and seed the papayas, set aside two wedges (for 8 servings) for garnish, and very finely dice the other flesh. Slit the chilies lengthwise and seed, set aside four halves (for 8 servings) for garnish, chop the others very finely.
Skin the garlic clove and press through a press. Peel the ginger and shallots and grate into the vinegar.
Crush the cumin and cloves in a mortar and stir with all the other ingredients. Mix the sauce and garnish with the chili peppers and papaya slices.