Preheat the oven to 400 degrees F.

Butter a 6-cup gratin dish and set aside.

Melt butter in a saucepan over medium heat.

Add flour to the melted butter and whisk until smooth.

Cook for 10 seconds.

Pour cold milk into the mixture in one stroke, whisking constantly.

Continue stirring with a whisk until the mixture thickens and comes to a strong boil (about 2 minutes). The mixture should be thick and smooth.

Remove from heat.

Stir in salt and pepper.

Allow the white sauce to cool for about 10 minutes.

Break eggs into a bowl and beat well with a fork.

Add the beaten eggs, grated cheese, and minced chives to the cooled sauce.

Mix well to combine all ingredients.

Pour the mixture into the prepared buttered gratin dish.

Bake for 30 to 40 minutes, or until the souffle is puffy and well browned on top.

Serve immediately for the best texture and enjoyment.