In a medium bowl, toss the carrots with the vinegar and sugar. Let stand at room temperature for 1 hour; stir occasionally.
In a food processor, combine the basil, anchovies, lime juice, fish sauce, crushed red pepper and chopped garlic and process to a paste. With the machine on, slowly pour in the olive oil and puree until blended. Season with salt and pepper. Let stand at room temperature for at least 30 minutes.
Preheat the broiler. Spread the cut sides of the baguettes with the butter. Toast 3 inches from the heat. Rub the toasted sides with the garlic clove; spread with the mayonnaise. Drizzle with the Sriracha. Arrange the cucumber, carrots and piquillo peppers on the bottoms and garnish with the cilantro. Spread the tops with the pesto and close the sandwiches. Cut in half and serve.