For the bread, preheat the oven to 300°F and line a baking sheet with parchment.
Beat the egg whites with the cream of tartar and salt until soft peaks form.
Whisk the cream cheese and egg yolk until smooth and pale yellow.
Fold in the egg whites a little at a time until smooth and well combined.
Spoon the batter onto the baking sheet into two even circles.
Bake for 25 minutes until firm and lightly browned.
To complete the sandwich, fry the egg in butter until done to your preference.
Arrange the sliced ham on top of one bread circle.
Top with the fried egg and the sliced cheese then the second bread circle.
Serve immediately or cook in a greased skillet to melt the cheese first.