Preheat the oven to 375 degrees and lightly butter (using 1 tablespoon of the butter) a 6 cup soufflé mold and a piece of foil (to wrap around the top of the soufflé pan), and dust with flour.
Combine the remaining 3 tablespoons of butter with the flour in a small pot and cook over medium low heat until the flour turns lightly golden, add the hot milk and whisk well to avoid lumps, add the egg yolks one at a time.
Place the egg whites in a large mixing bowl and beat on medium high until stiff peaks appear.
Fold in the egg whites 1/3 at a time and alternate with ½ of the Gruyere (reserve some to sprinkle on the top).
Place the soufflé in the oven and bake for 30 minutes, the soufflé is done when a skewer inserted in the middle, comes out clean.