Ground Beef Mixture: Form ground beef into an oval shaped patty. Place patty in a preheated sauté pan, season with salt and pepper, cook 3 to 4 minutes on each side. Using a spatula, coarsely chop patty on a crosshatch pattern. Add onions and mushrooms and sauté until softened. Coarsely chop vegetables into chopped meat. Place 1 slice American chees and 1 tablespoon shredded cheddar cheese on top of chopped beef vegetable mixture. Chop cheese into mixture allowing to melt.
Zodc Sauce: Place mayonnaise in a mixing bowl, slowly add dressing while mixing with wire whisk. Sauce should be thick not runny. Add remaining ingredients and mix until well blended.
For Service: Spread 1/2 teaspoon butter on crown of roll and 1/2 teaspoon butter on heel of roll. Place roll on preheated flat top grill, butter side down, to lightly toast. Remove toasted roll from grill, place beef and cheese mixture on heel of roll. Place 1/4 teaspoon jalapeno peppers on top of cheese. Spread 1 tablespoon mayonnaise on crown of roll. Place crown of roll on sandwich to close. Serve with 4-6 onion rings and zodc sauce.