The ponyshoe is the horseshoe re-engineered for one person to finish. It is the same open-faced Springfield plate, toast under meat under a pile of fries under a flood of cheese sauce, eaten with a knife and fork, but scaled down: a single slice of bread instead of two, less meat, a smaller heap of fries, and a proportionally smaller ladle of sauce. The defining fact is not that it is simply a half order. It is that the build is rebalanced so the smaller plate still works, because the horseshoe's appeal is its ratio of toast to protein to fries to sauce, and halving every component without re-tuning it would leave the base swamped.
The craft is in keeping a smaller base from dissolving under a sauce that does not scale down as gracefully as the bread. The single slice is still griddled or toasted firm, because it has to take fries and a ladle of cheese sauce without turning to paste before the fork reaches the bottom, and a thinner plate has less margin for that than the full build. The meat is the variable middle layer, a burger patty, ham, or fried chicken, sized so the bread is not overwhelmed. The fries go on hot so they stay crisp at the edges as long as possible against the sauce soaking up from underneath. The cheese sauce itself is the real test at any size: a smooth, glossy, pourable sauce that has to coat without breaking, and on a smaller plate the timing window between molten and congealed is shorter. Served slow, the fries go limp and the toast is gone before the meal is over, the same failure as the full size, reached faster.
The variations are the same open-faced, knife-and-fork logic at different scales and in different towns. The full horseshoe is the parent build; beyond Springfield, the Louisville Hot Brown puts turkey and bacon under a Mornay and a broiler, and the St. Louis slinger buries eggs and meat under chili rather than cheese. Each of those is a codified regional build with its own rules and its own town behind it, and each deserves its own article rather than being crowded in here.