In a large resealable plastic bag, combine the cucumbers, garlic, chili, sugar, 1/2 teaspoon of salt and 1 tablespoon of the lime juice. Seal and shake the bag squeezing slightly to mash the cucumber and release the juices . Let stand at room temperature for 30 minutes
Drain the cucumbers, reserving 2 tablespoons of the cucumber juice discard the garlic and chili In a medium bowl, whisk the cucumber juice with the remaining 1 tablespoon of lime juice and 2 tablespoons olive oil
Add the cucumbers, sliced radishes, and the herbs and season the salad with salt and pepper
Arrange the salad on plates. Place a piece of burrata or mozzarella alongside each serving, drizzle with the remaining 2 tablespoons of olive oil and serve.