Cut butter into six pieces and place water and butter in a medium saucepan. Bring to a full boil over medium heat just until butter has melted.
Add flour and salt all at once, stir vigorously until dough forms a ball and leaves the side of the pan, about one minute. Remove from heat.
Let stand five minutes. Add eggs, one at a time, mixing thoroughly after each addition, then mix vigorously 30 seconds longer. Stir in the shrimp, green onions and four tablespoons of Parmesan.
Drop shrimp dough by slightly rounded teaspoon about two inches apart on non-greased baking sheets. Sprinkle with remaining Parmesan
cheese and bake in a 400 oven 20 to 30 minutes or until puffed and golden brown. Serve warm or cooled. Makes about 18 puffs.