Toast the bread. Use a toaster or a hot dry skillet.
Toast until the slices are golden and sturdy. Spread a thin layer of mayo or butter on one or both slices if you like.
Heat the pan. Place a small nonstick skillet over medium heat. Add the butter or oil and let it melt and coat the surface.
Crack the egg. Crack the egg into the skillet.
Season with a pinch of salt and pepper. Let it cook undisturbed until the white is mostly set, about 1–2 minutes.
Flip or cover, depending on yolk preference. For a runny yolk, cover the pan and cook 30–60 seconds more (no flip). For over-easy or over-medium, gently flip the egg and cook another 20–60 seconds.
Add the cheese. Place the cheese slice over the egg in the last 20–30 seconds so it starts to melt.
If needed, cover the pan to help it along.
Assemble the sandwich. Place the egg and cheese on the toasted bread. Add any extras like hot sauce, avocado, or tomato. Top with the second slice.
Press and serve. Gently press the sandwich together so everything settles.
Slice in half if you like. Eat right away while it’s hot.