Pickle the vegetables. Combine vinegar, warm water, sugar, and salt in a jar and stir until dissolved. Add carrot, daikon, and jalapeno. Refrigerate for at least 1 hour, up to 1 week.

Make the aioli. Whisk mayonnaise, sambal, and lime juice together until smooth. Season with salt and set aside.

Marinate the chicken. Pound chicken to an even ½-inch thickness. Combine with fish sauce, soy sauce, sugar, garlic, and pepper. Marinate for 30 minutes or for up to 4 hours.

Make the caramel sauce. Combine sugar and 2 tablespoons water in a small saucepan over medium heat. Do not stir — swirl the pan occasionally. Cook until the sugar melts and turns a deep amber color, about 5 to 7 minutes.

Immediately and carefully add the fish sauce and 2 tablespoons water, it will bubble violently and seize. Lower the heat and stir until the caramel re-dissolves into a smooth syrup, 1 to 2 minutes. Stir in lime juice, ginger, garlic, and chili. Remove from heat and set aside.

Dredge the chicken. Whisk cornstarch, rice flour, salt, white pepper, and baking powder in a wide bowl. Drizzle in the cold water and use your fingers or a fork to mix until you have a shaggy, clumpy dredge. Press each chicken thigh firmly into the dredge, coating thoroughly on both sides. Let rest 5 minutes so the coating hydrates and adheres.

Heat ½ inch of neutral oil in a large cast iron or heavy skillet over medium-high until shimmering (about 350°F). Working in batches if needed, fry chicken 4 to 5 minutes per side until deep golden brown and cooked through. Transfer to a wire rack. While the chicken is still hot, brush or drizzle caramel sauce on top.

Assemble sandwiches. Spread sambal aioli generously on both sides of the buns. Place glazed chicken on the bottom bun, top with a heaping pile of drained pickled vegetables, and add a few cilantro sprigs. Close and serve immediately.