Add strips of chicken to a mixing bowl with salt, pepper and oil. Mix until evenly coated. Then weave onto skewers (2-3 straps per).
In a saucepan over medium heat, add butter. Once butter has fully melted, add garlic and saute about 3 minutes. Reduce heat to medium low and add all remaining ingredients, EXCEPT parmesan cheese. Let sauce simmer while grilling chicken.
Grill for 10 minutes then spin to other side and grill another 10 minutes.
Add parmesan cheese to sauce and stir well.
Brush sauce over chicken and let grill 3 minutes. Flip each skewer and brush again with sauce. Grilled 3 minutes more then remove from to platter or cutting board. Pour remaining sauce over top of chicken and let rest for 5 minutes before serving.