1. Cook bacon until brown and crisp and drain on paper towel. Set aside.
2. Swirl a tablespoon of olive oil in a skillet. Place 4 squares of bread, cut sides down, in skillet and cook over medium heat until brown (about 3 minutes). Set one slice on each plate.
3. Meanwhile, whisk together 1 tbsp of oil, shallots and vinegar in a bowl. Season with salt and pepper. Add arugula and toss.
4. Top each bread square with 2 slices of tomato and bacon (the more bacon the better).
5. Spray the same skillet with cooking spray (or use 1 tbsp of olive oil) and heat over medium. Once heated, crack eggs into the skillet. Sprinkle with salt and pepper and cook until whites are set and yolks are cooked as desired. If you would like them over-easy, flip the eggs when almost done and count to ten. Then remove them from the pan and place on top of the bacon.
6. Finish the open face sandwich off with the arugula and parmesan cheese. Serve with a knife and fork.