Chef Michel Bourdin reminded us, "Always remember that the guest has to wait for the soufflé, but the soufflé can't wait for the guest."
FOR THE SAUCE NANTUA:
3 tbsp. butter
3 tbsp. flour
2 cups hot milk
1 cup heavy cream
1/4 cup crustacean butter
Meat from 1 1-1.2-lb. boiled Maine lobster, cut into 1'' pieces
Salt and freshly ground white pepper
FOR THE SOUFFLÉ:
7 tbsp. butter
1/2 cup freshly grated parmigiano-reggiano
1/3 cup flour
1 cup hot milk
1/2 cup grated gruyère cheese
Freshly ground white pepper
1. For the sauce Nantua: Melt butter in a large saucepan over medium-low heat. Add flour and cook, stirring, for 2 minutes. Slowly whisk in hot milk, increase heat to medium, and cook, stirring constantly, until thickened, about 7 minutes. Add 1/2 cup of the cream and simmer, stirring, until reduced by one-quarter, about 6 minutes. Add remaining 1/2 cup cream and crustacean butter, stirring until melted. Add lobster meat and season to taste with salt and pepper. Cover surface with plastic wrap to prevent a skin from forming, and keep warm over very low heat.
2. For the soufflé: Preheat oven to 475º. Butter four 8-oz. soufflé dishes with 1 tbsp. of the butter, evenly coat insides with 1 tbsp. of the grated parmigiano, and refrigerate. Poach 4 of the eggs in a medium skillet of simmering salted water over medium heat for 3 minutes. Transfer eggs with a slotted spoon to paper towels to drain, then set aside.
3. Melt remaining 6 tbsp. of the butter in a large saucepan over medium-low heat. Add flour and cook, stirring, for 2 minutes. Gradually add hot milk, whisking until smooth and thick, 2–3 minutes. Remove pot from heat. Separate remaining 4 eggs, setting whites aside in a large mixing bowl. Whisk yolks into hot flour–milk mixture 1 at a time. Add gruyère, stirring until melted. Season to taste with cayenne, salt, and pepper. Transfer soufflé base to a large bowl. Working quickly, whisk reserved whites until they hold stiff peaks, then gently fold into soufflé base along with remaining parmigiano.
4. Spoon 1/3 cup of soufflé mixture into each dish. Add poached egg and 2 tbsp. of sauce Nantua with lobster to each. Spoon remaining soufflé mixture on top. Bake for 5 minutes, reduce heat to 400º, and bake until puffed and browned, about 10 minutes. Serve with remaining sauce.