Method
Once the butter is bubbling, pour in the beaten egg and a pinch of salt. Tilt the pan to spread the egg evenly.
Immediately place the two halves of the hamburger bun face-down onto the raw egg.
Once the egg is set and fully cooked, carefully flip the entire egg and bun assembly over in one piece.
Fold the edges of the egg that extend beyond the bun inward, so they sit neatly on top of the bread.
Place the kashar cheese slices on one half of the egg. Layer the salami, tomato slices, and lettuce on top.
Close the sandwich by folding the second half of the bun over the fillings. Press down lightly with a spatula to help the cheese melt.
Remove from the pan once the bun is golden brown and crispy. Serve hot!
Notes
Use a fresh Brioche bun for the best buttery texture. Cook over low-medium heat to ensure the eggs stay fluffy and don't brown too quickly before you flip them.