1. Bring a pot of lightly salted water to boiling. Add spaghetti and cook 10 minutes or as per package directions. Reserve 1 1/2 cups hot pasta water.
2. Meanwhile, add bacon to a large, lidded saute pan. Cook over medium heat for 6 minutes or until slightly crispy. While bacon is cooking, whisk together 2 of the eggs and the cheese in bowl. Add garlic to pan and cook 1 to 2 minutes.
3. When pasta has finished cooking, drain and immediately add to pan with cooked bacon and garlic. Toss for 1 minute to coat noodles. Remove pan from heat and stir in egg-cheese mixture and 1 cup of the reserved pasta water. Mix constantly for 2 minutes, making sure not to scramble the eggs. Stir in salt and pepper, cover and set aside.
4. Heat 1 teaspoon of the oil in a medium nonstick skillet. Add 2 of the eggs and fry sunny-side up for 3 to 4 minutes over medium heat; set aside. Repeat with remaining 1 teaspoon oil and 2 eggs. Divide pasta evenly among four bowls (if pasta seems a bit dry, stir in remaining 1/2 cup reserved pasta water just before serving). Place 1 egg on each serving and garnish with parsley.