Heat oil in skillet over medium-high heat. Add onion, zucchini, and red pepper and cook until soft and slightly charred. Add garlic and cook for one minute. Add eggplant and cook until soft, about five minutes. Stir in red pepper flakes and cook for one to two minutes. Add plum tomatoes, then stir in balsamic vinegar and tomato sauce, season with salt and pepper, and simmer for eight to ten minutes over medium-low heat.
Use a large spoon to make four separate wells in the ratatouille. Carefully crack an egg into each well. Sprinkle goat cheese evenly over ratatouille. Transfer to skillet to the oven and bake for eight to ten minutes, or until the whites of the eggs are set, but the yolks are still runny.
Garnish with basil and freshly ground pepper and serve with hunks of baguette.