Sauté the diced peppers and onion with the butter in a 12 inch cast iron skillet. (Or other similarly sized, oven safe pan. Cook them until tender.
When the peppers and onion are tender, spread them out on a plate to cool quickly so that you will be able to handle them, and also use the skillet.
While the peppers and onion are sautéing, use a filet knife or sharp pairing knife to cut a pocket in each chicken breast. Refer to the video in the post to see how I do that.
Stuff some of the sauteed peppers and onion mixture into a pocket in a chicken breast, and place it in the skillet. Repeat with all of the chicken breasts.
Sprinkle the chicken with the Cajun seasoninng, and any remaining peppers & onion.
Spread the shredded cheese over the top.
Bake for about 25 minutes, or until the chicken tests done with a meat thermometer - 165°(F).