In a large non-stick skillet over medium-high heat, bring the pasta sauce to a boil.
Gently break the eggs into the sauce. Cover, reduce heat to medium, and simmer for 5 minutes.
Remove skillet from heat and let rest, covered, for 5 minutes or until yolks are cooked to desired doneness.
Sprinkle with Parmesan cheese and fresh basil, if using.
Meanwhile, preheat the broiler to high. Brush both cut surfaces of baguette with olive oil and place on a baking sheet. Broil on the highest oven rack for 5 minutes, or until browned to desired doneness.
Serve with the eggs for dipping.