Place a tablespoon of butter in a microwave-safe cereal bowl (the bottom should measure 3.5 - 4 inches). Microwave until melted, about 30 seconds. Allow to slightly cool.
Using a fork, mix in one egg, 1 tablespoon of coconut flour, and ¼ teaspoon of baking powder. Microwave on high for 90 seconds.
Allow the bread to cool slightly, then carefully slice it into two slices.
Heat a nonstick skillet over medium heat. Spray it with olive oil spray. Break one egg into the skillet (use a greased egg ring or an egg pan if you want a round shape). Cook on both sides until done to your liking.
Add the two slices of bread, lightly browning them on each side.
Place one slice of bread on a plate. Top it with a slice of cheese, a slice of ham, and a fried egg. Place the second slice of bread on top. Serve immediately.
