Preheat an outdoor or indoor grill for low heat, and lightly oil the grate.
Sprinkle the chicken breasts generously on all sides with the Italian and grill seasonings. Slowly cook on the preheated grill, turning every 10 minutes; brush the chicken with the barbeque sauce each time you turn it. Cook until the chicken is no longer pink in the center and the juices run clear. Once done, an instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C).
While the chicken is cooking, melt the butter in a skillet over medium-low heat. Cook the onions, bell peppers, and mushrooms in the butter, stirring frequently until the vegetables are tender.
To make the sandwiches, place a chicken breast on each hamburger bun half. Spoon the pepper and onion mixture overtop, and top with a slice of Swiss cheese. Cover with the hamburger bun tops.
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