The Maxwell Street Polish is decided by the onions, not the sausage. A grilled Polish sausage goes into a bun under a heavy tangle of grilled onions and a stripe of yellow mustard, and that is the whole sandwich. The onions are the defining component. They are cooked down on the same flat-top as the sausage until they go soft and sweet and slicked with fat, and they are piled on in a volume that nearly matches the sausage itself, which is the textural and flavor signature that separates this from a plain sausage on a bun.
The craft is in the grill and the restraint. The sausage is a coarse, garlicky Polish link, griddled or flat-top cooked rather than boiled so the casing takes a snap and a charred edge, which is the firm, smoky spine the soft load needs. The bun is a plain soft roll chosen to disappear, there to hold the hand and soak up onion fat, not to compete. The grilled onions do double work: they are the dominant flavor and they are the moisture that keeps a dense sausage from eating dry, while the yellow mustard supplies the single sharp acid note that cuts through the fat and keeps the build from reading as heavy. There is nothing else on it on purpose. Built fast on a griddle and handed across a counter, it is a sandwich designed to be eaten standing up before the bun gives out under the onions.
The variations are small and stay inside the same grilled-onion frame. Sport peppers are the common addition, a hot pickled bite that adds acid and heat without changing the architecture; some builds add a swipe of relish or a few raw onions alongside the grilled. The broader hot dog family it sits in runs the same soft-bun-and-build logic with a frankfurter and an entirely different set of regional rules, the same idea spoken in a different city's accent. Each of those is a codified build with its own town behind it, and each deserves its own article rather than being crowded in here.