Bring to a good boil, water, wine, butter and salt. Remove from heat and mix in flour until it comes together. Return to the stove and stir swiftly on high heat until it forms a ball; for about 2 minutes. Transfer hot batter into a large bowl – let cool down a bit; stirring every so often.
Meanwhile, whisk eggs to combine. Pour one-third of the eggs into the still warm dough; mix well and add remaining eggs. Add cheese and season with black pepper and cayenne or chili pepper to taste.
Pipe out gougere into small sizes than large; about 1-inch (2.5cm) diameter puffs.
Unbaked pate a choux can be made in advance and stored in the freezer for weeks.
When needed, pop up frozen puffs in the oven and bake.
For best results, bake Pâte à choux using a preheated convection oven at 400ºF (190ºC) for about 15 minutes; do not over baked gougere nor open the oven door during baking; it will deflate.
Increase oven temperature to 450ºF (230ºC) if using conventional oven. Serve warm – Enjoy!