Heat the olive oil in a non-stick skillet over medium heat. Crack the eggs into the skillet and cook to your desired doneness, seasoning with salt and pepper. For sunny-side up, cook for about 2-3 minutes; for over-easy, flip and cook for an additional 1-2 minutes.
While the eggs are cooking, toast the slices of whole grain bread until golden brown.
Spread the mayonnaise evenly on one side of each slice of toasted bread.
On one slice of bread, layer the cooked bacon, followed by the sliced avocado.
Place the cooked eggs on top of the avocado, then add fresh arugula or spinach if desired.
Top with the second slice of bread, mayonnaise side down. Press gently to hold everything together.
Cut the sandwich in half and serve immediately.