Preheat the oven to 375℉.
Rub 1 tablespoon of softened butter onto the bottom and sides of a 1.5 quart round casserole dish. Then add 3 tablespoons of grated parmesan cheese to the dish. Turn the dish so that the parmesan covers all of the bottom and sides. Set aside.
Add the remaining 2 tablespoons of butter and flour to a pan and place over medium/high heat. Cook the flour and butter for about 1 minute until a golden paste has formed.
Add the heavy cream to the paste mixture, whisking vigorously. The cream should become thickened. Cook for another 2 minutes on low heat.
Transfer the thickened cream to a large bowl and mix in the dry seasonings.
Next, mix in the shredded gruyere cheese and the remaining parmesan cheese.
Add the egg yolks to the cheese mixture and mix until thoroughly combined. Set aside.
In a separate large bowl, add the egg whites and cream of tartar. Using a hand mixer, mix until soft peaks form. This took between 1-1.5 minutes with our hand mixer at full speed.
Gently fold the whipped egg whites into the cheese mixture. Then transfer into the greased souffle dish.
Bake for 30 minutes. When the souffle is done it should stand about an inch or two above the rim of the souffle dish. It will deflate slightly before serving.