Arrange chicken breasts in single layer in heavy skillet; add 4 cups water, basil sprig, onion, celery, bay leaf, one teaspoon salt. Heat uncovered on medium heat until water begins to boil; reduce heat to low. Simmer breasts covered 5 minutes. Remove skillet from heat. Uncover. Turn breasts over in hot broth. Recover. Let stand off heat for 5 minutes. Uncover again. Let chicken stand in broth for 10 minutes. Remove breasts to plate with slotted spoon. Remove skin and bones. Pull into 1" wide strips. Set meat aside covered. Pour broth into 4 cup glass measure. Return 1 cup of broth to skillet, reserve remainder for other use. Cook spaghetti in boiling water for 8-10 minutes. While pasta is cooking, add carrots to chicken broth in skillet; heat to simmering over medium low heat. Simmer carrots partially covered for 5 minutes. Add green beans, broccoli and peas; simmer still partially uncovered, until tender 5-8 minutes. Remove from heat, drain vegetables, reserving broth for other use. Wipe skillet dry. Melt butter in skillet over medium heat. When foam subsides stir in garlic, saute for 2 minutes. Add vegetables, chicken and spaghetti. Toss in butter until coated. Add more butter and salt to taste. Sprinkle with basil, and parmesan cheese.