In a small saucepan over high heat, bring the water, butter, salt, sugar and cayenne powder (optional) to a boil.
Take the saucepan off the heat, add the flour all at once and beat vigorously with a wooden spoon. Continue beating until the dough forms a solid, smooth mass and pulls away from the sides of the saucepan.
Quickly beat in the grated cheese to incorporate completely. Let batter cool 3 minutes.
Little by little add the beaten eggs, beating vigorously in between each addition, until the dough forms a smooth, shiny mass.
With a rubber spatula, scoop the "pate a choux" into a pastry bag and pipe out approximately 48 (1-inch) rounds, spaced 1 to 2 inches apart on the baking sheet lined with a silicon baking sheet or parchment paper.
Brush dough lightly with the other beaten egg and place in the oven. Cook until golden and puffed, about 25 minutes. Remove from the oven and cool briefly on a baking rack. Serve hot or at room temperature.
Video
Notes
The cayenne powder adds a wonderful, slight kick, but use less or omit if preferred.