How to Make It
Bring stock to a simmer in a medium saucepan over medium-low. Keep warm.
Heat butter and 1 1/2 tablespoons olive oil in a large saucepan over medium-high. Add onion and leeks; sauté 10 minutes. Add orzo; cook 2 minutes, stirring occasionally. Add wine; cook 1 minute or until liquid almost evaporates. Add 2/3 cup warm stock to pan; cook 3 minutes or until liquid is absorbed. Add remaining stock, 2/3 cup at a time, stirring occasionally until each portion is absorbed before adding more. Remove pan from heat; stir in parsley, 3 tablespoons chives, 1/4 cup Parmesan, salt, and 1/4 teaspoon pepper.
Heat a large nonstick skillet over medium. Add remaining 1 1/2 teaspoons oil to pan; swirl to coat. Crack eggs into pan; cook 2 minutes. Cover and cook 2 more minutes or until desired degree of doneness. Divide orzo mixture among 4 bowls; top each serving with an egg. Sprinkle evenly with remaining 1 tablespoon chives, remaining Parmesan, remaining 1/8 teaspoon pepper, and lemon rind.