Heat oven to 350 degrees. Cut 1/2 c. butter into 1 c. flour. Sprinkle 2 T. water over mixture. Round into ball; divide in half. On ungreased baking sheet, pat each half into a strip 12 x 3 inches in size, 3 inches apart.
Heat ½ c. butter and 1 c. water to rolling boil. Remove from heat; add flavoring. Beat in 1 c. flour until mixture forms a ball, stirring quickly, about 1 minute. Beat in eggs one at a time until smooth and glossy. Divide in half and spread each half evenly over strips.
Bake 45-60 minutes (or longer) or until topping is crisp and brown. DO NOT OPEN OVEN. Cool and frost with glaze. Sprinkle with nuts.
Combine ingredients and mix until smooth, then spread over puffs. Sprinkle nuts over glaze.