In a bowl, lightly mix the Swiss cheese, green onions, banana peppers, jalapeno peppers, and mayonnaise. Cover and refrigerate 24 hours to blend flavors. Mix in more mayonnaise before serving, if desired.
To serve, cut core out of cabbage and discard. Cut a thick slice from the bottom of the cabbage; use a fork to pull the inner leaves out of the cabbage to leave a hollowed out bowl. Pull several of the outer leaves slightly open and fold them back to make the bowl more attractive; serve the chilled dip in the hollowed cabbage.