Add about 1/4 of the egg whites to the base, and thoroughly fold them in to lighten the mixture (see note below about technique). Scoop the remaining egg whites onto the base, and gently fold the mixture together with a large rubber spatula. Between folds of the spatula, sprinkle in the grated cheese (Julia Child claims that this increases the souffle's lightness).
For a video demonstration of impeccable egg white technique by Jacques Pepin, check out the Lobster Souffle a l'Americaine, Part 2 episode of Julia Child's Cooking with Master Chefs series. The egg white whipping starts at about 17:18. With his remarkable technique, a copper bowl, and a balloon whisk, Chef Pepin is probably faster than my KitchenAid.
Adapted from Julia Child's master recipe for Cheese Souffle in The Way to Cook.