Preheat panini press. If not using a press, a griddle pan can be used, but you will need to flip your sandwich to cook both sides; tricky but possible.
Slice 2 - 1 1/2 inch slices of King's Hawaiian Round Bread. Spread mayonnaise on one slice, and mustard on the other slice of bread. Set aside.
Cut 2 slices of bacon in half. Using a large frying pan, fry until crispy. Drain on paper towels and reserve. Discard all but 1 TBS bacon grease in frying pan. All bacon grease can be discarded and the pan can be wiped clean with paper towels. Cooking spray, butter, or margarine can be used, but this recipe is not for the faint of heart--so go for the gusto and use the bacon grease!
Heat frying pan and cook egg to your liking. When done, remove from heat, but keep warm.
On the mayonnaise slice of bread, arrange bacon evenly. Add ham slices and half of the shredded Swiss cheese. Gently lay egg on top, then remaining cheese. Top with second slice of bread (mustard-side facing inside of sandwich).
Using silicone brush, lightly grease both sides of your heated panini press. Center sandwich and carefully close press--using spatula to keep bread slices from sliding apart. Cook until bread is toasted and cheese has melted.
Dig in and enjoy!