Combine the water, butter, salt, pepper, and cayenne in a large saucepan over medium-high heat and bring to a boil.
Reduce heat to medium-low and stir in the flour, continue stirring until the flour is well incorporated and starting to dry outa bit, about 3 minutes.
Transfer the flour mixture to bowl of a stand mixer or large mixing bowl and allow to cool, about 10 minutes.
Preheat the oven to 375°F and line a baking sheet with parchment paper.
Using the a stand mixer with a paddle or a wooden spoon, mix one egg into the flour mixture until well blended, continue with the remaining eggs one at a time until all the eggs are blended in.
Mix in the Parmesan cheese until thoroughly combined.
Scrape the dough into a pastry bag and pipe out about 24 even sized gougeres (a little bigger than a tablespoon) onto the parchment paper.
Wet your fingers and lightly press the gougeres to form even sized dome shapes.
Bake in the preheated oven for 35 to 40 minutes or until gougeres are golden brown.
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