Grate the Beemster Classic coarsely.
Melt the butter in a saucepan and stir in the flour. Simmer gently for 2 minutes and add the bouillon while constantly stirring. Continue stirring until the sauce is smooth and nicely thickened.
Remove from heat and stir in the cheese and chives and season with pepper to taste. Rinse a soup plate and pour the cheese sauce into it. Smooth out the surface and place the mixture in the refrigerator to set for 1 hour.
Slice the cheese mixture on the plate into 12 pieces and shape each piece into a small croquette. Dredge the croquettes in the egg first and then the breadcrumbs. Repeat once more.
The croquettes should be completely coated in breadcrumbs.
Heat the oil in the deep-fryer to 350 °F. Fry the croquettes in batches of 4-6 for 3-4 minutes until golden brown and done.
Place the croquettes on a paper towel to drain. Serve on a tray with a small bowl of mustard.