1. Preheat the oven to 425ºF (220ºC). Line a baking sheet with parchment paper or a silicone baking mat.
2. Heat the water, butter, salt, and pepper in a saucepan until the butter is melted.
3. Dump in the flour all at once and stir vigorously until the mixture pulls away from the sides into a smooth ball. Remove from heat and let rest two minutes, to cool it down a bit. At this point, you can scrape the dough into the bowl of a stand mixer fitted with the paddle attachment. If you don’t have a mixer, let it cool in the pan, stirring it a few times to let the heat escape.
4. Add the eggs, one at a time, stirring quickly to make sure the eggs don’t ‘cook.’ The batter will first appear lumpy, but after a minute or so, it will smooth out. After the eggs have been added, let cool until tepid. (So as not to melt the cheese in the next step.)
5. Add about 3/4s of the grated cheese, and stir until well-mixed.
6. Scrape the mixture into a pastry bag fitted with a wide plain tip and pipe the dough into mounds, evenly-spaced apart, making each about the size of a small cherry tomato.
7. Top each puff with a bit of the remaining cheese, the put the baking sheet in the oven.
8. Bake for 5 minutes, then turn the oven down to 375ºF (190ºC) and bake for an additional 20 to 25 minutes, until they’re completely golden brown.