In a small saucepan over medium heat, combine the bourbon, soy sauce, brown sugar, honey, ketchup, rice vinegar, garlic, paprika, and black pepper. Stir often and heat until the mixture thickens slightly, about 3-4 minutes. Remove from heat and let cool for 5-10 minutes.
Place the chicken pieces in a large bowl or zip-top bag. Pour the cooled marinade over the chicken, reserving ½ cup for later. Toss to coat the chicken, then cover and refrigerate for at least 1 hour, or up to 4 hours for a deeper flavor.
When ready, preheat the air fryer to 400°F.*
Working one skewer at a time, thread 4-5 chicken cubes onto each.
Arrange the skewers in a single layer in the basket of your air fryer. (Depending on the size of the air fryer, you may have to work in batches.)
Air fry at 400°F for 11-12 minutes, flipping halfway through. The chicken is done when it reaches an internal temperature of 165°F.
While the chicken cooks, bring the reserved marinade to a boil in a small saucepan. Let it simmer until it thickens into a glaze, about 3-5 minutes.
Brush the glaze over the cooked chicken skewers and garnish with fresh parsley.