Preheat the oven to 350 degrees F (175 degrees C). Line a baking sheet with parchment paper.

Combine 1 cup water, butter, and salt in a saucepan over medium heat and bring to a boil. Cook until butter has melted, about 5 minutes. Remove saucepan from heat. Add 1 cup plus 2 tablespoons flour all at once and mix vigorously with a wooden spoon until a smooth dough forms. Return saucepan to low heat; briefly cook and stir until dough pulls away from the pan and starts to dry out, about 2 minutes. Remove from heat and set aside to cool for 1 minute.

Beat eggs into the dough, 1 at a time, beating thoroughly after each addition. Add 1 cup grated Comte cheese and season lightly with pepper.

Use 2 teaspoons to place small mounds of dough onto the prepared baking sheet, leaving space between them.

Stir together egg yolk and 1 tablespoon water in a bowl and brush onto the dough mounds. Sprinkle with the remaining Comte cheese.

Bake in the preheated oven until puffed up and golden brown, about 20 minutes. Turn off heat and let gougeres cool in the oven with the door half-open.