Preheat the broiler and position a rack 6 inches from the heat. Brush the cut sides of the rolls with the butter.

In a small bowl, whisk 1/4 cup of the honey with the soy sauce, ginger, scallion, and chopped garlic. Season the honey glaze lightly with salt and black pepper. In another small bowl, whisk 1/4 cup of the honey with the vinegar and 1 teaspoon of salt. Add the carrots and toss to combine. In a third small bowl, whisk the mayonnaise with the sambal oelek and the remaining 1/4 teaspoon of honey; season the sambal mayonnaise with salt.

Arrange the fish fillets on a baking sheet; brush with oil and season lightly with salt and pepper. Broil for about 6 minutes, until the fish is just beginning to turn opaque. Brush the fillets very liberally with the honey glaze and broil for 8 minutes longer, until browned and cooked through.

Broil the buttered rolls for 1 minute, until they are toasted. Rub the whole garlic clove all over the toasted sides of the rolls and spread with the sambal mayonnaise. Using a slotted spoon, lift the carrots from the pickling liquid and spread them on the toasted rolls. Top with the glazed fish fillets, cucumber slices, and cilantro sprigs and close the sandwiches. Cut the sandwiches in half and serve right away.