Heat the vegetable oil in a skillet over medium heat. Stir in the garlic and onion; cook and stir until the onion has softened and turned translucent, about 5 minutes. Stir in zucchini; cook and stir for 5 minutes. Mix in the crushed tomatoes and hot pepper sauce. Cover and simmer for 10 minutes.
Make 4 wells in the tomato mixture, and crack the eggs into each well. Do not stir. Cover and cook until eggs are desired consistency, about 3 minutes for soft yolks. Carefully remove the eggs from the skillet and serve with the tomato sauce.