In a tall-sided large saucepan, heat the oil over medium heat. Add the onions and sauté until translucent, about 7 minutes. Add the garlic, red pepper, some salt and pepper, and sauté until fragrant, about 3 minutes. Add the eggplant to the pan and cook until softened slightly, about 5 minutes.
While the eggplant cooks, crush the tomatoes by hand and set aside for later use.
Add the tomato paste to the pan and cook until it becomes brick red, about 3 minutes. Add the tomatoes, oregano, and a bit more salt and pepper to the pan. Fill up the tomato can halfway with water and add to the pan. Cook, stirring occasionally, until the liquids reduce by about half, 45 minutes.
Create 8 little craters in the sauce. Crack the eggs, one at a time, into a small bowl or ramekin and place an egg in each spot created in the sauce. Sprinkle the eggs with some salt and pepper, and cover the pan until the eggs are cooked through, but still runny in the middle, 2 minutes. Serve with crusty Italian bread.