Pulse crushed fruit in a food processor a few times to create a rough puree—a little bit of texture is desirable.
Add oil, vinegar, lime juice, and a pinch of salt to the puree. Taste and adjust any of the seasonings. Chill for at least 1–2 hours before serving.
Serve in small bowls garnished with minced red onion, herbs, fresh pepper, a drizzle of oil, and an ice cube.