Fried Egg Sandwich

Breakfast Sandwich on Croissant Roll
When I was in high school I used to eat fried egg sandwiches at Vogt's Restaurant. They were inexpensive and Mrs. Vogt made a wonderful fried egg sandwich. It was made with just a fried egg and white bread, but Mrs. Vogt cooked the egg perfectly. I don't like runny yolks, but there was just a streak of undercooked yolk in the middle. In combination with the untoasted white bread, it was perfect.
On the other end of this very basic sandwich I used to eat, there is a world of variations.
1 Tbsp. butter
1 - 2 large eggs
Slice of cheese, such as Cheddar (optional)
2 slices of whole wheat or other bread (see below)
Butter for the toast
Melt butter in an 8" pan on medium heat. When it begins to foam and the pan is fairly hot, crack the egg(s) into the melted butter so as not to break the yolks. Turn the heat to medium and fry for about two minutes. Meanwhile, toast the bread and lightly butter each piece and place on a plate. Break the yolks and flip them over to cook the other side - you want to lightly brown each side of the egg, yet have the yolk remain a bit soft without being runny. If you want cheese on your sandwich (cheddar is a good choice), now is the time to add it. Then turn the heat off and cover with a lid until the cheese is nicely melted, but do not overcook the egg.
Place the egg(s) on a piece of toast, or other bread, butter side up, and add the other piece of toast, butter side down. Cut in two.
Variations
Other good additions beside the cheese is fried ham, bacon, sausage or Canadian bacon. Cook this first as it will take longer than the eggs to cook. Some people like to add ketchup to their sandwich. These folks often like to use untoasted white bread.
Other breads to use: English muffins, biscuits, bagels, challah-type roll, sesame-seeded hamburger bun, toasted/untoasted white bread, rye bread, wheat bread, croissant, etc.