Place the Bolognese into a skillet. Fill it about halfway full. Bring the Bolognese to a gentle boil over medium heat. Decrease the heat to medium-low and bring to a simmer.
Crack one egg into a small bowl. Set aside. Make a small depression in the Bolognese and gently pour the egg into this spot. Continue this process until all eggs are used (up to 5 or 6 depending up on the size of the skillet used).
Cover and cook over medium-low heat until the eggs are cooked to desired doneness., about 7 to 12 minutes.
Remove from the heat and top with grated parmesan and basil. Serve warm with crusty French bread.