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.
5. Add about 3/4s of the grated cheese and the chives, 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.