Set out the bread and cheese. Mix the mayonnaise with a pinch of black pepper if desired.
Melt 1 tablespoon of butter in a large nonstick skillet over medium heat. Toast the bread 1 to 2 minutes per side until golden, then transfer to a plate.
Add the remaining butter and reduce heat to medium-low. Crack in the eggs, season with salt and pepper, and cook about 2 minutes until the whites are set.
Flip the eggs and cook 30 to 60 seconds for over medium, or 1 to 2 minutes more for a firm yolk.
Place a cheese slice over two of the eggs, cover the skillet, and cook about 30 seconds until the cheese melts.
Spread mayonnaise on the toast. Layer a cheesy egg, optional tomato or spinach, and a second egg on the bottom slice. Top with the remaining bread, slice in half, and serve warm.