Preheat oven to 375 degrees F. Butter a 1.5-quart soufflé½½ dish. Coat with grated Parmesan.
Melt 4 tablespoons butter in a saucepan over medium heat. Whisk in flour and cook for 1-2 minutes.
Gradually whisk in milk. Cook, stirring constantly, until thickened (about 5 minutes).
Remove from heat. Stir in Gruyere, 1/2 cup Parmesan, Dijon mustard, nutmeg, salt, and pepper.
Whisk in egg yolks one at a time. Set aside.
In a clean bowl, beat egg whites with cream of tartar until stiff peaks form.
Gently fold 1/3 of egg whites into cheese mixture to lighten. Fold in remaining whites carefully.
Pour into prepared dish. Run thumb around the edge to create a "collar."
Bake for 25-35 minutes until puffed and golden. Do not open oven door during baking.
Serve immediately with fresh chives.