Preheat the oven to 400°F (200°C). Grease a soufflé dish with butter.
In a saucepan, melt 2 tablespoons butter over medium heat. Add flour and cook, stirring, for 1 minute.
Gradually whisk in the warmed milk, and continue whisking until thickened and smooth.
Remove from heat and stir in the salt, nutmeg, and half of the Gruyère cheese until cheese is melted.
In a separate bowl, beat the egg whites until stiff peaks form.
Mix the egg yolks into the cheese sauce, then gently fold in the beaten egg whites.
Spoon the mixture into the prepared soufflé dish, sprinkle with remaining Gruyère cheese on top.
Bake in preheated oven for about 25 minutes, or until puffed and golden brown. Serve immediately.