Preheat the oven to 400°F. Generously butter four 6-ounce ramekins and coat the inside with grated Parmesan cheese, tapping out the excess.

In a medium saucepan, melt the butter over medium heat. Stir in the flour and cook, stirring constantly, for 1-2 minutes to create a roux.

Gradually whisk in the milk and cook, stirring constantly, until the mixture thickens and coats the back of a spoon, about 2-3 minutes.

Remove the saucepan from the heat and stir in the grated Gruyère and Parmesan cheeses, salt, and black pepper until the cheeses have melted and the mixture is smooth.

In a separate bowl, whisk the egg yolks until light and frothy. Slowly pour the cheese mixture into the egg yolks, whisking constantly to prevent the eggs from scrambling.

In a large, clean bowl, beat the egg whites and cream of tartar with an electric mixer until stiff peaks form.

Gently fold one-third of the egg white mixture into the cheese mixture to lighten it. Then, fold in the remaining egg whites until just combined, being careful not to over mix and deflate the batter.

Divide the soufflé batter evenly among the prepared ramekins, filling them almost to the top.

Place the ramekins on a baking sheet and bake for 12-15 minutes, or until the soufflés have risen and are golden brown on top.

Serve the egg soufflés immediately, garnished with fresh herbs or a light dusting of grated Parmesan cheese, if desired.