In large saucepan, saute garlic in butter. Stir in the cream and 1 teaspoon parsley. Combine cornstarch and water until smooth; stir into cream mixture. Bring to a boil; cook and stir for 2 minutes or until thickened.
Remove from the heat; stir in parmesan cheese until melted. Toss with linguine; sprinkle with salt, pepper and remaining parsley.