Heat olive oil over medium heat in large deep skillet. Cut zucchini and squash in half length wise and cut into 1/2 inch pieces. Rough chop onion and red pepper. Add to skillet and cook till just crisp tender. Then add tomatoes, tomato paste and greek seasoning. Simmer for 10 minutes over medium heat.
Add balsamic vinegar, sugar and salt & pepper to your taste. Use the back side of a ladle to make a well in the ratatouille. Gently crack egg in well. Repeat until all 4 eggs are in the simmering liquid. Put a lid on the skillet and cook an additional 2-4 minutes.
Ladle ratatouille into a shallow bowl, tear basil leaves on top and serve with crusty cheesie garlic bread.