Heat the olive oil in a frying pan over medium heat. Add the onions. Cook, stirring frequently, until soft and almost caramelized. Remove the onions with a slotted spoon and set aside. In the same frying pan, add the eggs and fry to desired doneness. Sprinkle with salt and pepper. Spread the bread with the mustard or mayo.

Place the bacon on the bottom slice of bread. Top with the fried eggs. Place the cooked onions on top along with the cheese. Top with top piece of bread. Serve immediately.