Combine tuna, onion, bell pepper, jalapeno, eggs, and gerkins. Stir in mayonnaise, mustard, and pickle juice; add salt and pepper, to taste. Adjust seasonings if necessary.
Preheat oven to 375 degrees. Place dinner roll halves on a large cookie sheet. Top each with a large spoonful of the tuna salad mixture, using the spoon to spread/flatten. Bake in oven for about five minutes, then remove.
Lay a slice of cheese on top of each roll. Return pan to the oven and turn on broiler. Watching carefully, broil until cheese is melted and bubbly. Remove from oven and serve immediately.