Heat a non-stick skillet over medium heat and add the butter, letting it melt and coat the pan.

Crack the eggs into the skillet and sprinkle with salt and black pepper. Cook sunny-side up or to your preferred doneness (about 2-3 minutes). Remove eggs and set aside.

In the same skillet, place the slices of bread and toast them for about 1 minute on each side until lightly golden.

Sprinkle shredded cheese evenly onto one slice of bread in the pan. Place the cooked eggs on top of the cheese, then cover with the second slice of toast to form a sandwich.

Press the sandwich lightly with a spatula and cook for about 1-2 minutes on each side, until the cheese is melted and the bread is golden brown.

Remove the sandwich from the skillet, slice it in half, and garnish with avocado slices if desired. Serve warm.