Preheat the oven to 220°C / 425°F (200°C fan) and line two baking trays with parchment paper.
Combine the water, butter, and salt in a medium saucepan, bring to a boil over medium-high heat, and stir until the butter is fully melted.
Remove the pan from the heat, add the flour, nutmeg, and black pepper, stir quickly until the mixture comes together, then return to low heat and cook for 1 minute while stirring to dry the dough slightly.
Take the pan off the stove, let the mixture cool for 2 minutes, then beat in one egg at a time, mixing well after each addition until the dough is smooth and glossy.
Stir in the shredded cheese until evenly combined, then drop tablespoon-sized mounds of dough onto the prepared trays, leaving space between each puff.
Brush the tops with the beaten egg yolk, sprinkle with the extra shredded cheese, and bake for 25 minutes until the puffs are golden and crisp.
Let the cheese puffs cool on the trays for about 15 minutes so the insides set a little, then serve warm as snacks, appetizers, or alongside soups and stews.