Heat the oven to 375°F and arrange a rack in the bottom third. Generously coat a 6-cup soufflé dish with butter and sprinkle it lightly with breadcrumbs to coat evenly; set aside.
Melt butter in a small saucepan over low heat. When it foams, add flour and stir occasionally until flour has cooked slightly, about 4 minutes. Gradually whisk in milk and bring to a boil, stirring frequently. Remove from heat and whisk in salt, pepper, and nutmeg.
Whisk egg yolks in a large bowl until smooth. Whisk about 1/3 cup of the milk mixture into yolks until smooth. Add remaining milk mixture, whisking until blended. Stir in cheese and set aside. Place a baking sheet in the oven to heat while finishing the soufflé, at least 5 minutes.
Place egg whites in the bowl of an electric mixer fitted with the whisk attachment and beat on medium speed until soft peaks form, about 5 minutes. Increase the speed to high and beat until peaks are stiff and smooth but not dry, about 2 minutes more.
Gently fold 1/3 of the egg whites into the cheese mixture until blended and no white streaks are visible. Add remaining whites and chives and gently fold until thoroughly combined. Pour into the prepared soufflé dish.
Place soufflé on the heated baking sheet. Bake until it is well risen, the top is browned, the edges appear dry, and the center is set (it doesn’t move if lightly touched), about 35 to 40 minutes. Serve immediately.
Beverage pairing:Charles Heidsieck Brut Réserve, France. Since the only thing that goes well with airy is more airy, the natural pairing for this dish is Champagne, preferably one that is a little smoky and cheesy as only Champagne can be. Charles Heidsieck makes a wine in this style due to its aging methods. You’ll find that the mature notes of pastry, flint, and lemon go wonderfully with this light, pungent soufflé.