To prepare the rémoulade: In a medium bowl whisk together the rémoulade ingredients, including Tabasco sauce and salt to taste. Cover and refrigerate until ready to serve.
Brush each of the crabs on both sides with melted butter. Season them with salt and pepper to taste. Grill the crabs over Direct High heat until the shells are bright red, 4 to 6 minutes, turning once halfway through grilling time. Serve immediately with the rémoulade.