Gougères

Preheat the oven to 400°. Sprinkle 2 large rimmed baking sheets with flour. In a medium saucepan, combine the water with the butter and salt and bring to a boil over moderate heat until the butter melts. Add the 1 1/3 cups of flour and beat constantly with a wooden spoon until a smooth, thick paste forms. Continue beating until the dough pulls away from the side of the pan and forms a ball, about 1 minute. Remove the pan from the heat and let the dough cool slightly, about 10 minutes. Add 4 of the eggs, 1 at a time, beating well after each addition. Stir in the cheese.

Drop rounded tablespoons of the dough onto the prepared sheets, about 1 inch apart. Beat the remaining egg in a small bowl. Brush the gougères with the beaten egg and bake for about 30 minutes, or until puffed and browned. Transfer the gougères to a platter and serve warm.