Using a butter knife and 1/2 tablespoon of the butter, coat one side of each slice of bread.
Heat a skillet over medium heat and, when hot, add the bread slices, buttered side down, to one side of the skillet.
After 30 seconds, add the remaining 1/2 tablespoon of butter to the other side of the skillet and, when melted, add the ham and egg to the skillet.
Season the egg with the salt and pepper. Using the edge of a spatula, pierce the egg yolk so that it runs. Allow to cook until the egg begins to firm and the ham browns, about 30 seconds.
Using the spatula, flip both the ham and the egg and continue to cook until both are done, about 30 seconds longer.
Using the spatula, stack the ham and egg on one unbuttered side of the toast, and top with the other slice, buttered side up.
Use the spatula to remove the sandwich from the skillet, transfer to a plate, and serve.
YIELD: 1 serving