How to Make It
Preheat the oven to 400°. Butter and flour six 1 1/2-cup ramekins.
In a medium saucepan, melt the 2 tablespoons of butter. Add the minced shallots and cook over moderate heat, stirring constantly, until softened, about 2 minutes. Add the 2 tablespoons of flour and cook, whisking constantly, for 30 seconds. While whisking, add the milk in a slow, steady stream; whisk in the salt and piment d'Espelette and season with black pepper. Cook over moderate heat, whisking, until the mixture comes to a simmer and is slightly thickened, about 5 minutes. Remove the saucepan from the heat and stir in the cheese until it is melted.
Transfer the soufflé base to a large bowl and let cool slightly. Whisk in the egg yolks, one at a time, until incorporated and no streaks remain. Let cool to room temperature, about 15 minutes.
In a large stainless steel bowl, using an electric mixer, beat all of the egg whites at high speed until firm peaks form. Fold one-third of the whites into the soufflé base to lighten it, then fold in the remaining whites until no streaks remain.
Spoon the soufflé base into the prepared ramekins, filling each one about three-fourths full. Bake the soufflés for 12 to 13 minutes, until puffed, just set and golden on top. Serve immediately.