In a medium saucepan, combine the water, 1/4 cup butter and 1/4 teaspoon salt. Bring to boiling. Add flour all at once, stirring vigorously. Cook and stir until mixture forms a ball. Remove from heat. Cool for 10 minutes.
Add eggs, one at a time, beating well with a wooden spoon after each addition. Stir in all but 1 tablespoon of the cheese. Drop dough by large spoonfuls, forming 10 mounds in a 10-inch ring on a greased 12-inch pizza pan. Sprinkle the remaining 1 tablespoon of cheese over top of cream-puff dough.
Bake in a 400 degree F oven for 40 minutes or until puffed and golden. Cool on pan on a wire rack. When cool, use a serrated knife to cut ring in half horizontally. Remove and discard the weblike centers, if you like.
In a small bowl, combine 2 tablespoons softened butter, the snipped Italian parsley, snipped chives, 1/4 teaspoon salt, and pepper. Set aside.
In a 12-inch skillet, heat remaining 2 tablespoons butter over medium heat. (Add additional butter, if needed, during cooking.) Add carrots and cauliflower; stir-fry for 3 minutes. Add remaining vegetables and stir-fry 3 to 4 minutes or until all vegetables are crisp-tender.
Remove vegetables from skillet. Add chicken and snipped basil to the skillet and stir-fry 3 to 4 minutes or until chicken no is longer pink. Return all vegetables to skillet; add butter mixture and toss to coat.
To serve, place bottom half of cream puff ring on a serving plate. Spoon chicken-and-vegetable mixture over bottom half of the cream puff ring. Replace the top of the ring. Spoon any remaining chicken and vegetable mixture in the center of the ring. Garnish with sprigs of basil, Italian parsley and whole chives, if you like. Serve immediately. Makes 5 servings.