Preheat oven to 375 F.
In a saucepan set over medium heat, melt butter. Brush a small amount of melted butter up the sides of a 1-quart souffle dish. Sprinkle grated Parmesan around the dish, rolling to cover all sides. Discard excess. Place the dish in the refrigerator until ready to use.
With the saucepan still set over medium heat, stir the flour into the remaining melted butter. Cook for 2 minutes while stirring; do not let it brown. Whisk in hot half-and-half, stirring constantly until thickened. Bring to a vigorous simmer. Remove from heat and stir in cheese and spices until smooth.
In a medium bowl, beat egg yolks. Temper with the cheese mixture by adding a few tablespoons of the hot mixture at a time, whisking between each addition. Once half of the cheese mixture is added, pour the rest into the yolks and stir well. Let cool to room temperature.
In a stand mixer or in a medium bowl, beat egg whites until just foaming. Add cream of tartar and a pinch of salt, then beat until glossy with firm peaks.
Fold a third of the egg whites into the yolk mixture, combining completely. Repeat in two batches, folding gently to incorporate and not deflate the egg whites. Pour the batter into the prepared souffle dish. Bake on the lower rack of the oven 22-25 minutes until browned and just set. Serve immediately.