Special equipment: a 10-by-15-inch broiler-safe rimmed baking sheet
Position an oven rack 4 to 5 inches from the heating element, and preheat the broiler. Brush a 10-by-15-inch broiler-safe rimmed baking sheet with oil.
Put the turkey, egg, breadcrumbs, scallions, fish sauce, red pepper flakes, 1/2 teaspoon salt and a few grinds of black pepper in a large bowl, and mix gently, just enough to incorporate evenly. Drop mounds of the mixture all around the prepared baking sheet, and press them into an even layer. Score the meat into 24 even squares, cutting down almost all the way. Brush the top with the hoisin sauce. Broil until the meat is browned and glazed and registers 165 degrees F on a meat thermometer, 8 to 9 minutes.
Carefully pour off any excess liquid from the cookie sheet. Rescore the meat into 24 sliders, then follow the score lines with a spatula to divide. Top each slider with a cucumber slice and a cilantro leaf.
While the sliders are cooking, arrange the lettuce, remaining cilantro, carrots, onions and lime wedges on a serving platter. Put the peanuts and Sriracha if using in small serving bowls. Slide a spatula in the pan and let guests build their sliders with their desired toppings.
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