Melt butter in small frying pan. Add onions and jalapeños and sauté until tender.
While the onion and jalapeño mixture is cooking, sprinkle both sides of hamburger patties with cajun seasoning.
Pop burgers onto the grill and grill for about 5 minutes.
Flip burgers and place cheese slices on meat so that it will melt. Continue cooking burgers until they reach desired doneness.
Spread mayonnaise onto jalapeño-ciabatta bread (if you can't find jalapeño ciabatta bread, regular ciabatta bread will do in a pinch!)
Place finished burgers on buns and pile high with the onion and jalapeño mixture.
Serve with sliced tomatoes, lettuce and pepperoncini peppers.