Preheat oven to 375 degrees F. In a food processor, purée the cream cheese and salmon, and set aside. Using a pastry brush, brush the soufflé dish with two tablespoons of softened butter; then coat with breadcrumbs, shaking off excess. (The breadcrumbs will give the soufflé a rough surface to adhere to as it rises, allowing for a taller soufflé.) Set aside. Mince the shallot and reserve 3 tablespoons.
Make the béchamel sauce: In a saucepan over medium heat, add five tablespoons of butter, followed by the shallot. Sauté until translucent, 1½ minutes, making sure the shallot doesn’t take on any color. Lower the heat, add the flour, and cook, stirring continuously until the flour is no longer raw. This is the “roux,” the base of béchamel sauce. Season with salt, pepper, and nutmeg. While the heat is on medium-low, slowly whisk the milk and cream into the roux to create the béchamel sauce. When the sauce has thickened to a gravy consistency, scrape into a bowl to cool.
Make the soufflé base: Separate the eggs into whites and yolks, one at a time; you'll be using all 7 egg whites but only 6 egg yolks. (Use the last yolk for another dish.) Stir the yolks into the béchamel sauce, followed by the salmon-cream cheese mixture. Mince the chives and add 3 tablespoons to the mixture; chop the dill and add 1 tablespoon; finally, thinly slice the green onions on a bias and fold those in as well. Set aside.
Whip the egg whites and assemble the dish: In a clean, non-copper mixing bowl, add the egg whites and whisk until foamy. Add cream of tartar and continue whisking to the "soft-peak" stage, about 2 minutes. Continue whisking until egg whites are at the "hard-peak" stage, when the peaks hold their shape, about 30 more seconds; do not overmix. Mix a third of the whites into the soufflé base to lighten the base. Then lay the remaining egg whites on top, and gently fold them in by running a rubber spatula around the outside of the bowl and cutting through the center to drape the base over the top of the whites. Do not fully incorporate: some of the egg whites should be visible to keep the soufflé light and airy. Pour the mixture into the prepared dish, gently place on a baking sheet, and bake in the middle of the oven for 50 minutes (no peeking!).
Remove from the oven and serve: When the soufflé is puffed and golden, remove and serve immediately. (If you want your guests to see the soufflé in its full glory, have them come to oven and watch as it first comes out!)