Heat the oil in a large, nonreactive skillet over medium heat, add the onion, and cook for 5 minutes, or until soft. Add the zucchini and eggplant and cook for 3 to 4 minutes more, or until soft. Add the garlic and paprika and cook for 1 minute. Add the tomatoes and bring to a simmer. Add salt, pepper, and balsamic vinegar, to taste, and simmer for 7 to 8 minutes.
With the back of a large spoon, make four depressions in the ratatouille. Drop 2 teaspoons of pesto into each. One at a time, crack each egg into a small bowl, then slide the egg into a depression. Cover the skillet and cook for 4 to 6 minutes, or until the eggs are done to your liking. Garnish with parsley and olives before serving.