Papayas are ripe when they are just slightly soft, like a ripe pear. Ripe papayas are wonderful with a squeeze of lime or lemon juice.
Pureed with orange juice, they make a thick, delicious smoothie, and a smoothie of nothing but perfectly ripe papaya and milk is popular in Asia and outrageously delicious, says kobetobiko. They’re also great with pureed with yogurt and honey, or cottage cheese, or vanilla ice cream.
marlie202 halves papayas, adds a bit of butter and cinnamon to the cavity, and bakes them.
On the savory side, try them with feta, or with ranchero cheese, salt, and lime juice.
piccola likes them in salads with dark greens, water chestnuts, almonds, and a spicy dressing (like chili-lime or sesame-ginger). Theresa makes a composed salad made up of successive layers of watercress dressed with lemon juice and olive oil, buffalo mozzarella drizzled with olive oil, cubed papaya, and Parma ham.