1. Heat a large nonstick skillet over medium-high heat. Add oil; swirl to coat. Add onion, potatoes, and herbes de Provence; spread mixture in a single layer in pan. Cook 4 minutes, without stirring, or until potatoes are lightly browned.
2. Reduce heat to medium. Stir in zucchini, yellow squash, beans, salt, and 3/8 teaspoon pepper; cook 3 minutes. Remove pan from heat; cover and let stand 5 minutes. Stir in tomato, chives, and parsley.
3. Add water to a large skillet, filling two-thirds full; bring to a boil. Reduce heat; simmer. Stir in vinegar. Break each egg into a custard cup. Gently pour eggs into pan; cook 3 minutes or until desired degree of doneness. Carefully remove eggs from pan using a slotted spoon. Divide squash mixture evenly among 4 plates; top each serving with 1 egg. Sprinkle eggs evenly with remaining 1/8 teaspoon pepper and Parmesan cheese.