Place chicken wings in a large mixing bowl. Toss wings with olive oil, Kosher salt, and black pepper, then set aside. If using a spice seasoning or dry rub, add olive oil to wings, but omit the salt and pepper.
Preheat a smoker or pellet grill. Place wings directly on the grates, allowing excess oil to drip over the mixing bowl, then cook over direct heat. Serve immediately, with sauces, if using.
Preheat a gas grill over medium-high heat. Place wings directly on the grill grates, allowing excess oil to drip over the mixing bowl, then cook over direct heat until an internal temperature of 165F is reached. Serve immediately, with sauces, if using.