In a large skillet cook onion, chile pepper, and garlic in hot oil over medium heat about 5 minutes or until tender. Add tomatoes, zucchini, dried savory, and salt; cook about 5 minutes or until tomatoes release their liquid and zucchini is tender.
Break one of the eggs into a measuring cup. Carefully slide egg into the tomato mixture. Repeat with the remaining three eggs, allowing each egg an equal amount of space in the tomato mixture. Cover and simmer over medium-low heat for 3 to 5 minutes or until whites are completely set and yolks begin to thicken but are not hard. Sprinkle with queso fresco. If desired, garnish with fresh cilantro sprigs and/or serve with corn tortillas.