In a 10-inch skillet, heat the oil over medium heat. Add the onion, 1 sprig of parsley and the garlic and cook, stirring, until the onion softens, about 5 minutes. Add the vinegar and let it evaporate completely. Add the tomatoes and their juices and bring to a boil over medium heat. Cook until slightly reduced, about 10 minutes. Remove the garlic and parsley sprig.
Add the chopped parsley and basil to the sauce. Break the eggs into the sauce, cover, and simmer for 5 minutes. Remove from the heat, let sit for 5 minutes, then serve.