How to Make It
Whisk together vinegar, lime zest and juice, honey, salt, pepper, and 2 tablespoons of the oil in a small bowl until well combined. Toss together tomato slices and 2 tablespoons of the vinegar-lime mixture in a medium bowl; set aside. (Reserve remaining vinegar-lime mixture.)
Cut honeydew melon in half; remove and discard seeds. Cut each melon half into 4 wedges; remove rinds. Shave melon wedges into thin ribbons using mandoline.
Arrange tomato slices, shaved melon, and burrata on a large platter. Drizzle with reserved vinegar-lime mixture. Sprinkle with sliced mint, and drizzle with remaining 1 tablespoon oil. Serve immediately.