Cut peppers and onion into strips
Cube chicken
Heat oil over medium heat
Add chicken and cook until half cooked stirring in seasonings and searing the outside
Pull chicken to edges of pan
Add sliced vegetables to pan and cook until tender
While vegetables cook, cook pasta per instructions
Once vegetables become tender, clear a space in the middle of the pan and add cheese wedges one at a time breaking them up so they melt.
Combine everything in pan coating it with cheese.
Add 1/3 cup of pasta water (or more depending on how much liquid you prefer)
Drain pasta and stir into rest of mixture
Serve topped with pepper jack cheese