Heat oil in a large nonstick skillet over medium heat. Add onion; cook 6 minutes or until tender, stirring occasionally. Add tomatoes; cook 1 minute, stirring occasionally. Add eggplant and next 3 ingredients (through Chili-Espresso Rubbed Steak); cook 3 minutes or until heated. Stir in salt and 1/4 teaspoon pepper. Keep steak mixture warm.
Add water to a large skillet, filling two-thirds full. Bring to a boil; reduce heat, and simmer. Add vinegar. Break eggs into pan; cook 3 minutes or until desired degree of doneness. Carefully remove eggs from pan using a slotted spoon. Spoon about 1 1/2 cups hash onto each of 4 plates; top each serving with 1 egg. Sprinkle evenly with remaining 1/4 teaspoon pepper and parsley.