In a medium bowl, whisk together the mayo, sweet chili sauce, sriracha, honey, lime juice, and a pinch of salt until smooth and well combined. Taste and adjust the balance of heat and sweetness to your preference—I find that the lime juice really brightens the sauce, so don't skip it. Reserve this sauce for serving and topping.
In a large bowl, combine the ground chicken, Panko breadcrumbs, 1 tablespoon of the bang bang sauce from Step 1, chopped cilantro, sliced green onions, freshly minced garlic, smoked paprika, salt, and black pepper. Mix gently with your hands until just combined—don't overmix, as this can make the patties tough and dense. The mixture should hold together but feel light.
Divide the chicken mixture from Step 2 into 4 equal portions and gently shape each into a patty about 3/4-inch thick. For pan-frying: Heat a large skillet over medium-high heat with a thin coat of oil. Cook the patties for 5-7 minutes per side until they reach an internal temperature of 165°F. For air-frying: Place patties on the air fryer basket and cook at 400°F for 15 minutes, shaking the basket halfway through. I find that pan-frying gives better browning and a more flavorful crust than air-frying, so that's my preferred method.
While the patties cook, warm a skillet over medium heat and lightly butter the cut sides of the brioche buns. Toast them for 1-2 minutes until golden and fragrant. Arrange your fresh toppings on a plate: wash and pat dry the butter lettuce leaves, slice the tomato into 1/4-inch rounds, and thinly slice the red onion.
Spread a generous amount of the bang bang sauce from Step 1 on both halves of each toasted bun. Layer a butter lettuce leaf on the bottom bun, top with a cooked patty from Step 3, then add tomato slices and red onion. Drizzle additional sauce over the patty if desired, then cap with the top bun. Serve immediately while the patties and buns are still warm.