Finely grate the cheese. Finely dice ham. Peel onion, dice finely and fry in hot butter until transparent. Sauté 5 tbsp. flour in it until light yellow. Stir in milk, bring to the boil while stirring and simmer for about 4 minutes. Melt cheese in the sauce. Stir in ham. Season sauce with salt and pepper. Spread into an oiled flat dish and let it cool down. Chill for 2-3 hours
Whisk egg, salt and pepper. Form approx. 20 croquettes from the cheese mixture with floured hands. Turn them one after the other in the breadcrumbs, egg and again in the breadcrumbs. Chill for about 1 hour
Heat the oil in a deep fryer or a high pot to approx. 180 °C. Fry the croquettes in it in portions for about 5 minutes until golden brown. Drain on kitchen paper. Serve hot or cold