Preheat the oven to 425 degrees. Line a baking sheet with parchment paper or silicone baking mat.
Heat the water and butter in a saucepan until the butter is melted.
Pour 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.
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. (You can transfer the mixture to a bowl before adding to eggs to cool the dough, or do this step in a food processor or electric mixer, if you wish.) Add about 3/4s of the grated cheese and stir until well-mixed.
Scrape the mixture into a pastry bag fitted with a wide plain tip, or a Ziploc bag with the corner cut off and pipe the dough into mounds, evenly-spaced apart, about an inch-and-a-half in diameter.
Top each puff with a bit of the remaining cheese, then pop the baking sheet in the oven.
Bake for 10 minutes, and then turn the oven down to 375 degrees and bake for an additional 20 to 25 minutes, until they’re completely golden brown and cooked through.
To serve, slice a completely cooked puff almost all the way through. Spoon a small scoop of ice cream in each. Place on a serving dish and drizzle with a generous amount of honey. Sprinkle with crunchy salt to taste.