Preheat the oven to 425F. Line a baking sheet with parchment paper or a silicone mat. Heat the water, butter, salt, and pepper in a saucepan over medium heat until the butter has melted but not quite boiling. Dump the flour in all at once and stir vigorously until the mixture pulls away from the sides of the saucepan into a smooth ball.
Remove from the heat and let rest two minutes. Add the eggs, one at a time, stirring quickly to make sure the eggs don’t scramble. The batter may seem lumpy at first, but after a minute or so, it will come together and smooth out.
Add ¾ of the grated cheese, and the thyme, and stir to combine. Scrape the mixture into a pastry bag fitted with a wide plain tip and pipe the dough into mounds, evenly-spaced, making each about the size of a cherry tomato.
Top each puff with a bit of the remaining cheese then place the baking sheet in the oven. Bake for 5 minutes, and then turn the oven down to 375F and bake for an additional 15 to 20 minutes, until they’re completely golden brown. For extra-crispy puffs, 5 minutes before they’re done, poke the side of each puff with a sharp knife to release the steam, and return to the oven to finish baking.