Season the chicken wings. Pat the thawed chicken wings dry with paper towels. In a small bowl, combine smoked paprika, garlic powder, onion powder, kosher salt, and black pepper. Toss the wings with the seasoning until evenly coated.
Make the Coca-Cola barbecue sauce. In a medium bowl, whisk together Coca-Cola, barbecue sauce, apple cider vinegar, Worcestershire sauce, and minced garlic.
Add to the slow cooker. Arrange the seasoned wings in a greased 6-quart slow cooker. Pour the Coca-Cola BBQ sauce evenly over the chicken.
Slow cook the wings. Cover and cook on low for 3-4 hours or high for 2-3 hours, until the chicken reaches an internal temperature of at least 165°F and is tender.
Remove the wings. Carefully transfer the cooked wings to a foil-lined baking sheet. Arrange them in a single layer with the skin side facing up.
Reduce the sauce. Pour approximately 1½ cups of the slow cooker cooking liquid into a saucepan. Bring to a full boil, then reduce the heat and simmer for 10-15 minutes to concentrate the flavor.
Thicken the glaze. Whisk cornstarch and cold water together in a small bowl. Stir the mixture into the simmering sauce and cook for another 2-3 minutes, until thick and glossy.
Coat the wings. Preheat the oven broiler to high. Brush the thickened Coca-Cola BBQ glaze generously over the chicken wings.
Broil the wings. Place the baking sheet approximately 6-8 inches below the broiler. Broil for 3-5 minutes, watching closely, until the glaze bubbles and begins to caramelize.
Garnish and serve. Remove the wings from the oven. Brush with additional warm glaze if desired. Garnish with sliced green onions or parsley and serve immediately.