Mix the white wine vinegar with mustard, olive oil, lime juice, salt and pepper until creamy.
Cut the papaya in half lengthwise. Remove the seeds with a spoon. Remove the flesh from the skin with a baller.
Cut the avocados in half lengthwise and remove the stones. Loosen the flesh from the halves, also using the baller.
Arrange the papaya and avocado balls on a platter and drizzle with the dressing on the spot. Sprinkle with parsley.
Similar fare is loved elsewhere in the Caribbean. On St. Lucia, for example, a leaf salad of papayas is served, dressed with olive oil, green onions, chilies, pepper and garlic. On St. Maarten, avocados are combined with cucumbers, and on Puerto Rico, avocados with oranges, onions and olives.