Melt butter in a saucepan over medium heat.

Add flour and milk, stirring until creamy.

Add egg yolks, one at a time, stirring well after each addition.

Remove from heat.

Add parmesan cheese, gruyere cheese, salt, and pepper.

Mix well to combine.

Spread the mixture into a greased 9x9 inch pan.

Freeze until firm enough to cut into squares.

Beat egg whites until frothy.

Dip the frozen cheese squares into the beaten egg whites.

Then, coat the squares with breadcrumbs.

Deep fry the breaded squares until golden brown.