For the wings: Preheat the oven to 450 degrees F.
Toss the chicken wings with some salt and pepper and then place the wings on a parchment-lined baking sheet. Roast to an internal temperature of 165 degrees F, 12 to 15 minutes. Let cool. (At this point, the wings can be refrigerated for up to 24 hours.)
In a small bowl, mix together the brown sugar, thyme, allspice, onion powder, turmeric, cayenne and 2 teaspoons kosher salt. Set aside.
Heat 2 inches of peanut oil in a large Dutch oven over medium-high heat until a deep-fry thermometer registers 350 degrees F. In batches, fry the chicken wings until just crispy, 2 minutes. Remove to a paper-towel-lined plate to drain. While the wings are still hot, add them to a large bowl and sprinkle with a generous amount of the jerk spice mixture. Toss until well coated.
For the remoulade: In a small bowl, mix together the mayonnaise, mustard, sriracha, Worcestershire, garlic, lemon zest, lemon juice and 1 tablespoon of the jerk spice mixture.
Serve the wings with the remoulade on the side.