Coat the ramekins: Using a pastry brush, paint the insides of four 8-oz ramekins with softened butter, using firm vertical strokes from bottom to rim. Chill for 10 minutes, then apply a second butter layer the same way. Add the grated Parmesan, tilt each ramekin to coat the inside completely, and tap out the excess. Chill the ramekins until you need them.
Build the bechamel base: Melt the butter in a heavy saucepan over medium heat. Whisk in the flour and cook, stirring constantly, for 1 to 2 minutes until it smells nutty and turns pale gold. Pour in the warm milk a little at a time, whisking hard after each addition so no lumps form. Simmer for 3 to 4 minutes, stirring, until the sauce is thick enough to coat the back of a spoon.
Melt in the cheese: Take the pan off the heat and stir in the Gruyere, the extra Parmesan, the Dijon mustard, cayenne, salt, and black pepper until the cheese melts into a smooth, glossy sauce. Let it cool for 5 minutes — it should be warm, not hot — then beat in the egg yolks one at a time until fully combined.
Whip the whites: Place the egg whites in a spotlessly clean, completely dry large bowl. Add the cream of tartar and a tiny pinch of salt. Beat with an electric mixer, starting on medium and increasing to high, until the whites form stiff, glossy peaks that stand straight up when you lift the beaters.
Loosen, then fold: Stir about one-third of the whipped whites into the cheese base with a whisk to loosen it. Switch to a large rubber spatula and gently fold in the remaining whites in two additions, cutting down the middle, sweeping around the bowl, and turning the bowl as you go. Stop the moment you cannot see any white streaks.
Fill and score the edge: Divide the mixture evenly among the prepared ramekins, filling each one right to the top. Tap each ramekin once firmly on the counter to settle the batter, level the tops with a palette knife, then run your thumb around the inside rim of each ramekin to make a shallow trench.
Bake without peeking: Place the ramekins on a baking sheet and bake in a preheated 400°F oven for 15 to 18 minutes, until the tops are deeply golden and risen well above the rims, with just a slight wobble in the center when you gently nudge the tray. Do not open the oven door for the first 15 minutes.
Serve at once: Dust the tops with a little extra grated Parmesan and carry the souffles straight to the table. A souffle waits for no one — it begins to settle within minutes, so have your guests seated and your salad ready before it comes out of the oven.
