In a medium fry pan, add a splash of water, soy sauce, and vinegar, to mostly coat the bottom of the pan; season with pepper and cayenne. Add a pat of butter.
When the broth is a rolling boil, crack in 4 eggs. Consider seasoning the egg yellows.
Lower heat to mid-high and occasionally poke holes thru the inner egg whites; to help them cook.
When egg whites are 90% set, add cheese and attempt(but fail) to fold.
After a bit, slide it out of the pan.