Place 3 tablespoons smoked paprika, 1 1/2 tablespoons kosher salt, 1 tablespoon black pepper, 1 tablespoon cayenne pepper, 1 tablespoon garlic powder, 1 tablespoon onion powder, and 1 tablespoon Italian seasoning in a small bowl and stir to combine.

Pat 4 pounds chicken wings dry with paper towels and place on a baking sheet. (If you plan to roast the wings in the oven, line the baking sheet with aluminum foil first.) Sprinkle the spice rub all over the chicken. Cover and refrigerate 4 to 24 hours. Meanwhile, make the BBQ sauce.

Place 2 1/3 cups ketchup, 1/4 cup packed dark brown sugar, 3 tablespoons apple cider vinegar, 1 1/2 tablespoons Worcestershire sauce, 1 tablespoon garlic powder, 1 tablespoon onion powder, 1 tablespoon ground cumin, 1 tablespoon chili powder, 1 1/2 teaspoons kosher salt, 1 teaspoon celery seeds, 1 teaspoon liquid smoke, 1/2 teaspoon cayenne pepper, and 1 bay leaf in a medium saucepan.

Bring to a boil over medium heat, stirring to combine. Reduce the heat to maintain a simmer and cook, stirring occasionally, for 25 minutes. Remove from the heat and discard the bay leaf. Add 1 tablespoon unsalted butter and whisk until melted and combined. Let cool and refrigerate in an airtight container until ready to use.

Let the chicken sit at room temperature for 1 hour before grilling. About 20 minutes before the chicken is ready, heat an outdoor gas grill for direct and indirect heat by heating half the burners to medium heat (about 375ºF) and half the burners on to medium-high heat (about 400ºF). For a charcoal grill, create two-zone cooking by piling the lit coals onto one side of the grill.

Scrape the grill grates clean. Oil the grill grates with a paper towel dipped in vegetable oil. Place the wings flatter-side down on the hotter side of the grill, leaving space between each wing for the heat to circulate. Cover and grill for 10 minutes. Flip the wings, cover, and grill for 10 minutes more.

Transfer a few wings to a large bowl, pour in just enough BBQ sauce to coat the wings, and toss with tongs until coated. Return the wings to the cooler side of the grill. Repeat until all the wings are coated.

Cover and grill for 10 minutes more to let the sauce heat up and caramelize on the wings. This sauce contains a good amount of sugar, so watch the wings closely to prevent scorching. The wings are ready when they register at least 165ºF on an instant-read thermometer. Brush with more sauce before serving.

Let the chicken sit at room temperature for 1 hour before roasting. Arrange two racks to divide the oven into thirds and heat the oven to 400ºF. Line a second baking sheet with aluminum foil.

Transfer half the chicken onto the second baking sheet. Arrange all the chicken flatter-side up in a single layer and space them apart evenly. Roast for 20 minutes. Remove the chicken from the oven and brush all over with the BBQ sauce. Flip the chicken so the wings are flatter-side down.

Increase the oven temperature to 450ºF. Return the chicken to the oven and roast for 8 minutes. Repeat flipping and brushing the chicken all over with the BBQ sauce, and continue to roast until the chicken is cooked through and registers at least 165ºF on an instant-read thermometer, and the sauce begins to caramelize, about 8 minutes more. Serve with the remaining BBQ sauce.