Melt 1 tablespoon butter in a large skillet over medium-high heat, then add leeks and cook, stirring often, until softened and bright green, about 3 minutes. Season with salt and pepper; let cool. (Leeks can be made 1 day ahead and refrigerated.)
Butter a 9-by-13-inch baking dish. Place 1/2 cup Parmesan in dish, and tilt dish to coat bottom and sides well. Pour out and discard excess cheese.
In a heavy saucepan over medium heat, melt 1 stick butter. Whisk in flour and cook, whisking constantly, for 1 minute or until well combined and heated. Gradually add milk, whisking constantly until batter is very smooth. Add 1 teaspoon salt, season with pepper, and continue whisking until soufflé base is smooth, shiny and thick, about 12 minutes.
Preheat oven to 400º. Transfer soufflé base to a bowl, and beat in egg yolks 1 at a time, beating thoroughly after each addition. Add Gruyere, the remaining Parmesan, leeks and herbs and beat until well combined.
In the bowl of a stand mixer using the whisk attachment, beat egg whites with 1/2 teaspoon salt until stiff peaks form (you can also do this by hand if you don’t have a stand mixer, though it will take a little longer!) Fold whites gently but thoroughly into soufflé base, one-third at a time (a few streaks of whites may remain and that’s fine.) Spoon soufflé mixture into baking dish; bake until puffed and golden, 35 to 40 minutes.