Preheat oven to 375 degrees F (190 degrees C).
In a heavy saucepan bring water to a boil with butter and salt over high heat and reduce heat to moderate. Add flour all at once and beat with a wooden spoon until mixture pulls away from side of pan. Cook mixture over medium heat to dry out the paste. As it cooks, push the paste from side to side with the wooden spoon. You will know when the paste is dry when it begins to leave a thin film on the bottom of the saucepan. Transfer mixture to a bowl and with an electric mixer on medium speed to release some of the steam. Continue to mix and slowly add eggs 1 at a time, beating well after each addition. Batter should be stiff enough to just hold soft peaks and fall softly from a spoon. If batter is too stiff, in a small bowl beat remaining egg lightly and add to batter, a little at a time, beating on high speed, until batter is desired consistency.
Stir Gruyère into pâte à choux.
Lightly grease 2 baking sheets or line with parchment paper.
Drop level tablespoons of batter onto prepared sheets about 1 inch apart on baking sheets.
Bake in upper and lower thirds of oven, switching positions of sheets halfway through baking, 30 minutes, or until puffed, golden and crisp.
Gougères keep, chilled in zip-top plastic bags, 2 days or frozen 1 week. Reheat gougères, uncovered, in a preheated 350 degrees F (180 degrees C) oven 10 minutes if chilled or 15 minutes if frozen.