Bring 3 cups water and 1/4 teaspoon salt to a boil in large saucepan. Add asparagus; cook 5 minutes or until crisp-tender. Remove asparagus with a slotted spoon; rinse under cold water, and set aside. Add rice and butter to cooking liquid; cover and simmer 15 to 20 minutes or until done. Set aside.
Combine 1/4 teaspoon salt and eggs in a small bowl, stirring with a whisk until well-blended. Add 3/4 cup cheese, 3 tablespoons chives, basil, lemon rind, and pepper; stir well. Stir egg mixture into hot rice. Stir in asparagus; cook rice mixture over low heat for 1 minute or until mixture is thoroughly heated. Top with 1 tablespoon each of cheese and chives.