1. Preheat a gas or charcoal grill to medium heat. Season the avocados with salt and pepper and rub with the olive oil and lime juice. Place the avocados flesh side down on the grill and cook for 5 minutes.
2. Arrange the tomato slices on a serving platter and generously season with salt and pepper. With a large soup spoon, remove the avocado halves from their skins and slice about 1⁄2 inch thick. Alternate the avocados with the tomatoes on the platter.
3. For the dressing, whisk together all of the ingredients, season with salt and pepper, and drizzle over the salad.