Blanch carrots: Fill a glass 3-cup measuring cup with ice and cold water. Set a small saucepan of water over high heat. When the water boils, add carrots and blanch for 30 seconds. Drain carrots and plunge into ice bath. Allow the carrots to remain in the water while you continue making the salad.
To make the lime vinaigrette, zest 1 lime into a small bowl and then juice both limes into the bowl with zest. Whisk in vinegar, oil and shallots. Season with salt and Tabasco to taste.
In a medium bowl, toss together basil, scallions, crabmeat, carrots and capers. Spoon in half of the lime vinaigrette and gently fold everything together to coat the ingredients.
Spoon the crabmeat salad onto the plates, garnish each plate with approximately half a sliced avocado and a basil sprig. Lightly spoon a bit more vinaigrette over the avocados, sprinkle with Maldon salt and freshly ground black pepper. Garnish with microgreens or sunflower sprouts.