In a 10- to 12-inch frying pan over high heat, stir oil, onion, and turkey until meat is browned and crumbly, about 7 minutes.
Add curry powder; stir until fragrant, about 30 seconds. Add papaya, broth, and chutney. Cover and cook over medium heat, stirring occasionally, until papaya is tender when pierced, 5 to 7 minutes.
Mix cornstarch and 2 tablespoons water; stir into pan. Keep stirring until sauce boils, about 1 minute. Add salt to taste. Scrape into a bowl.
To eat, spoon turkey mixture into lettuce leaves and roll up.
Nutritional analysis per first-course serving.