Gammon and egg is the cured-ham-steak sandwich with a fried egg set on it, and the egg is there to do one job: be the sauce. A gammon steak is dense, firm, and heavily salted from the cure, and on its own between bread it reads as one strong, dry note with nothing to lubricate it. A fried egg with a soft yolk solves both problems at once. The yolk breaks under the first bite and runs into the meat and the bread as a rich, unsalted sauce, and the soft white adds a yielding layer against a firm steak. The defining fact of this build is that the egg is not a second filling sitting alongside the gammon; it is the moisture and the foil the salted steak was missing.
The craft is the steak and the yolk timed against each other. The gammon is grilled or fried until the fat catches and the meat is cooked through, then cut so it is not a single tough plank, because a yolk sauce cannot rescue a steak that fights the bite. The egg is fried with the white fully set and the yolk still liquid, since a hard yolk turns the build back into two dry things stacked together and forfeits the whole reason the egg is there. Soft plain bread carries the weight, and butter on it is structural, sealing the crumb and carrying the heavy salt of the cure across into the wheat before the yolk arrives to soften everything further. It is closed and eaten while the yolk is still slack, the cut edge tipped up so the sauce runs back through the meat rather than straight out.
The variations are the same steak with the counter changed. A ring of pineapple swaps the soft yolk for a sweet acid that cuts the salt rather than coating it; mustard or a sharp pickle does the cutting in a dry register with no sauce at all; the plain gammon sandwich is the base with nothing added, the salt left to stand on its own. Each is the cured steak meeting a different answer to the same problem, and they deserve their own articles rather than being crowded in here.