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1
Combine the water, milk, butter, and salt in a heavy saucepan. Bring to a rolling boil over medium heat, ensuring the butter is fully melted before the liquid boils away. The surface should be turbulent and the butter completely incorporated.
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2
Remove the pan from the heat, add all the flour at once, and stir vigorously with a wooden spoon until a rough paste forms. Return to medium heat and continue stirring for 2–3 minutes, pressing the paste against the base and sides of the pan — the desséchage, or drying-out stage. The paste is ready when it forms a smooth, cohesive ball that pulls cleanly away from the sides and a thin dry film coats the base of the pan.
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3
Transfer the paste to a bowl and allow it to cool for 2–3 minutes. Beat the eggs in one at a time, incorporating each egg fully before adding the next — the paste should return to a smooth, uniform mass between each addition. This is where the dish lives or dies: paste that receives eggs too quickly, or that has not been sufficiently dried, will be slack and loose and the gougères will not puff. The finished paste is smooth, glossy, and drops from the spatula in a thick, slow ribbon.
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4
Fold 90 g of the grated cheese into the warm paste until evenly distributed. Reserve 30 g for topping.
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5
Heat the oven to 200 °C. Line two baking trays with parchment. Pipe or spoon the paste into mounds of approximately 3 cm diameter, spacing them 4 cm apart. Scatter the reserved cheese over each mound. The mounds should be neat and regular — no larger than 3 cm, as larger portions will be doughy at the centre.
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6
Bake for 20–22 minutes without opening the oven during the first 15 minutes. The gougères are done when they are deeply golden, fully puffed, and crisp to the tap of a fingernail. Turn off the oven, crack the door, and leave them inside for 5 minutes to set gradually and prevent collapse.
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7
Rest on a wire rack for 10–15 minutes before serving. The exterior should be crisp; the interior hollow with a thin, slightly moist, eggy lining. Serve warm. The cheese flavour fades and the texture turns rubbery once cold.