Melt butter in a pan, add garlic & peppers first. Simmer for 3-5 minutes, add mustard & peach jam. Simmer for about 3 more minutes.
Preheat the grill to medium heat, about 350-375 degrees F. Salt and pepper the chicken wings liberally on all sides.
Once the grill is hot, place the wings on the grill and cook for 7-9 minutes per side. If the chicken wings you buy are very small, grill for just 6 minutes per side.
Flip the wings. Brush glaze over the top side of each wing and grill another 3-5 minutes. Then flip one last time, and brush the wings with glaze. Grill another 3-5 minutes.
Take the wings off the grill. Then brush all remaining glaze over the wings. Serve warm.