►Heat oven to 375°F. Butter insides of ramekins generously. Mix breadcrumbs and 2 tablespoons Parmigiano Reggiano. Sprinkle mixture into each ramekin to completely coat sides and bottoms. Cut 6 long strips of parchment paper and wrap one around each ramekin; trim to leave a 2-inch lip above the rim of each ramekin. Secure parchment paper with butcher’s twine.

►Warm milk in a small saucepot over medium-low heat. Meanwhile, melt butter in another small saucepot over medium heat. Stir flour into melted butter and cook, stirring, until mixture resembles wet sand, about 3 minutes. Whisk in warm milk. Bring mixture to a boil, stirring constantly, then reduce heat and simmer for 5 minutes. Remove mixture from heat and stir in salt, white pepper, cayenne, and mustard. Add egg yolks and whisk immediately to avoid clumps. Whisk in Gruyère and remaining Parmigiano Reggiano and set aside.

►Whisk egg whites with cream of tartar in a bowl until stiff peaks form. Fold one-third of egg whites into warm cheese mixture. Fold in remaining egg whites until fully combined. Do not overmix; batter should be light and airy, without large pockets of egg white.

►Portion soufflé batter into prepared ramekins. Place on a rimmed baking sheet and transfer to oven. Bake for 20 to 25 minutes, until soufflé centers are set but still have a slight jiggle. Open oven door very gently to ensure soufflés don’t deflate. Serve immediately.