Preheat your oven to 350°F (175°C) and set an oven rack in the middle position.

Use the softened butter to generously grease a 2-quart (2-L) soufflé dish, coating well. Sprinkle in ¼ cup (25 g) of the Parmigiano-Reggiano and roll it around so the dish is lined with cheese.

In a small saucepan over medium heat, melt the 3 tablespoons of butter. Once melted, add the flour, cooking and whisking constantly for about a minute until slightly pale.

Gradually whisk in the cold milk, stirring until smooth and thickened, which should take a few minutes.

Once thickened, remove from heat. Stir in salt, black pepper, and nutmeg. Mix in Cheddar and remaining Parmigiano-Reggiano until melted and smooth, then cool for about 10 minutes.

Whisk in the egg yolks and chopped chives until well blended.

In an electric mixer, whip the egg whites with the cream of tartar until foamy. Increase speed to medium-high and whip until stiff peaks form, about 3 minutes.

Gently fold one-third of the cheese mixture into the egg whites until smooth, then carefully add the rest without deflating the whites.

Pour the mixture into the prepared dish, filling no more than an inch from the top. Place the dish on a baking sheet and bake for about 35 minutes until puffed and golden brown.

Serve immediately for maximum fluffiness, as it might collapse after being removed from the oven.