In a small cup or bowl, mix together flour and 3 tablespoons milk until smooth. Pour remaining milk into a large saucepan over low heat. Whisk in flour mixture and cook, stirring constantly, for 5 minutes or until the mixture thickens. Remove from heat and stir in cheddar cheese, 1/4 teaspoon salt, and cayenne pepper. Transfer to a large bowl and let cool.

Preheat oven to 180°C / 160°C (fan oven) / 350°F / Gas Mark 4. Whisk egg yolks into the cooled cheese mixture until well combined.

In a large glass or metal bowl, whip all 4 egg whites until foamy. Add remaining ¹⁄₄ teaspoon salt and continue beating until stiff peaks form. Stir 1 of the egg whites into the cheese mixture. Gently fold in remaining egg whites with a rubber spatula until just combined. Transfer mixture to an ungreased souffle dish.

Bake for 30-35 minutes or until the souffle is puffed and cooked through. Serve immediately.