^ The hamburger you are describing is not that of the Miamisburg Hamburger Stand. They have no cheese to put on their burgers.
They do fry (but not "deep fry") their burgers in a large iron skillet. They are the size of White Castle Sliders. All toppings are optional, albeit limited. Salt, pepper, onion (which can be strong), and pickle. That's it. No cheese or sauces (ketchup, mustard, mayo, 1000 Island Dressing, etc).
Although the price has increased A LOT over the years, they are some kick a$$ non-traditional burgers!