Make the meatballs: Preheat the oven to 375°F.
In a large bowl, combine the ground chicken, hot sauce, brown sugar, paprika, salt, black pepper, cayenne, and garlic and gently mix with your hands until combined.
Divide the meat mixture into 12 portions, then form them into meatballs using wet hands. (Meat sticks to dry hands.) Push a piece of cheese into each meatball and pinch the meat mixture around it to enclose the cheese.
In a large ovenproof sauté pan, heat the butter and vegetable oil over medium heat until combined and shimmering, about 2 minutes. Add the meatballs and brown on all sides, 5 to 8 minutes. Transfer the pan to the oven and bake for 10 minutes to finish cooking the meatballs.
Meanwhile, make the sauce: In a small saucepot, combine the butter, hot sauce, honey, and brown sugar. Bring to a boil over high heat, stirring continuously, then reduce the heat to medium and cook until the mixture comes together, 2 to 3 minutes. Remove from the heat, add the garlic powder, salt, and pepper and stir until smooth.
Remove the meatballs from the oven and pour the sauce over them. Toss to coat. Sprinkle with the parsley. Add a pickle chip to each bun, then set a meatball on top. Skewer with a toothpick. Serve warm.
