How to Make It
In a medium bowl, combine 2 tablespoons of the lime juice with the grapeseed oil, brown sugar, lime leaves, lemongrass, ginger and fish sauce. Add the shrimp and toss, then refrigerate for 2 hours, stirring occasionally.
Meanwhile, squeeze the cucumber to remove as much liquid as possible. Transfer to a small bowl and add the yogurt, shallot, coriander, cayenne, half of the minced garlic, 1 tablespoon of the mint, 1 tablespoon of the cilantro and 1/2 teaspoon of the lime zest. Season with salt and pepper and refrigerate for 1 hour.
In a medium bowl, toss the melon slices with 1/2 tablespoon of the lime juice and the remaining 1 tablespoon of mint and 1/2 teaspoon of lime zest; season with salt and pepper. Refrigerate until chilled.
In another medium bowl, mash the avocados with the onion, chile and the remaining garlic, 1 tablespoon of lime juice and 2 tablespoons of cilantro. Season with salt and pepper.
Preheat a grill. Drain the shrimp well. Grill over high heat, turning once, until browned, about 4 minutes. Transfer the shrimp to a platter and serve with the yogurt sauce, melon and avocado puree.