Preheat your oven to 350°F (175°C).

Use softened butter to grease a 2-quart soufflé dish, sprinkle ¼ cup of Parmigiano-Reggiano inside to coat.

Melt 3 tablespoons of butter in a small saucepan over medium heat and add flour, whisk for about 1 minute.

Gradually pour in the cold milk while whisking to avoid lumps, cooking until it thickens and comes to a boil.

Stir in salt, pepper, and nutmeg. Incorporate Cheddar and remaining Parmigiano-Reggiano until smooth.

Cool for 10 minutes, then whisk in egg yolks and chives.

In a separate bowl, beat egg whites and cream of tartar until foamy, then increase speed to medium-high until stiff peaks form.

Fold the beaten egg whites into the cheese mixture in thirds until fully incorporated.

Pour the mixture into the prepared dish, filling to about 1 inch from the top.

Bake on a baking sheet for about 35 minutes, or until puffed and golden brown. Serve immediately.