Preheat the oven to 375°F (190°C). Grease eight ramekins or oven-safe dishes with butter.

In a saucepan, melt the butter over medium heat. Add the flour and cook for about 1 minute, stirring constantly, until it forms a smooth paste.

Gradually whisk in the milk and continue cooking for another 2 minutes, or until the mixture thickens.

Remove the saucepan from heat and let it cool slightly.

Separate the egg yolks from the egg whites. Set the whites aside for later.

In a mixing bowl, whisk the egg yolks. Slowly add the cooled milk mixture, grated cheddar cheese, grated Parmesan cheese, salt, and black pepper. Stir until well combined.

In a separate bowl, beat the egg whites until stiff peaks form.

Gently fold the beaten egg whites into the yolk mixture until fully incorporated.

Divide the mixture equally among the prepared ramekins or dishes.

Place the ramekins on a baking sheet and bake for about 20-25 minutes, or until the souffles have puffed up and turned golden brown.

Serve immediately while the souffles are still hot and puffy.