Cut and discard the dark green part of the leek. Cut the rest of the leek in half lengthwise and rinse it under cold water, then chop it finely.

Heat the oil in a saucepan over medium heat until it’s hot, then sauté the leek for 3 minutes, covered.
Continue cooking over high heat, uncovered, for 3 to 4 minutes, stirring occasionally, until the leek is tender and the liquid has evaporated.
Remove from heat and let cool completely.

Preheat the oven to 425 F (220 C).
Prepare 2 baking sheets by lining them with parchment paper.

In a large saucepan, heat the water, butter, salt, dry mustard, and Cayenne pepper over medium heat until the water is hot and the butter has melted.
Add the flour, then continue cooking for 5 minutes, stirring often, until the mixture forms a ball.
Put the ball in the bowl of an electric mixer.
Add the eggs one by one, until the mixture is smooth.
Add the cheese and cooled leeks, and mix well.

Drop the dough by spoonfuls onto the prepared baking sheets, forming small mounds, using a piping bag without a tip or two soup spoons.
Make sure to space them at least 2″ (5 cm) apart.

Bake for 10 minutes, then reduce the oven temperature to 375 F (190 C) and continue baking for 20 minutes.
Remove the gougères from the oven and let them cool slightly before serving.