1. Butter a 1 1/2-2-quart (2l) baking dish generously. Dust the bottom and sides with Parmesan cheese.
2. To make the soufflé base, Melt the butter in a medium saucepan. Stir in the flour and bring to a low boil. Cook until the mixture has thickened a bit, 1 to 2 minutes. Turn off the heat, whisk in the warm milk and turn the heat to medium-high and bring to a boil, whisking frequently. Once the mixture comes to a boil, cook for 1 minute, whisking constantly.
3. Remove from heat and whisk in the salt, a generous amount of freshly ground pepper, nutmeg, and cayenne. Whisk in the egg yolks vigorously, one at a time. Scrape the mixture into a medium to large bowl and let cool a bit until only slightly warm.
4. To make the soufflé, preheat the oven to 400ºF (200ºC.) Reserve a handful of the cheese, and stir the rest of the cheese and chives into the soufflé base. In a large, clean bowl, or in the stand mixer with the whip attachment, whisk the egg whites with a pinch of salt until they hold their shape but are still moist and creamy. Don’t overbeat them.
5. Fold one-quarter of the beaten egg whites into the soufflé base thoroughly, then fold the remaining egg whites in just until there are no (or few) visible streaks of egg whites. Scrape the mixture into the prepared baking dish, gently smooth the top, and strew the reserved handful of cheese over the top.
6. Bake the soufflé on the middle rack of the oven for 20 minutes, without opening the oven door. Depending on how you like your soufflés, if you like them on the soft, somewhat runny side, it’s probably done. If you like them firmer, usually 25 minutes (total) is the right baking time. The best way to check it to touch the center at the 20 minute mark. If the soufflé still jiggles and moves freely in the center when you touch it, it’s done, if you like softly-cooked soufflés. If not, put it back in the oven for another 5 minutes.