Melt the butter in a pan and whisk in the plain flour. Over a gentle heat, gradually whisk in the milk until you have a very thick white sauce. Add the fresh breadcrumbs, chopped ham, grated cheddar, torn mozzarella and the chopped parsley and stir until melted. Chill for 4 hours.
Scoop up spoonfuls of the mixture and roll into 18-20 oval shapes. Roll each first in plain flour, then coat in beaten egg, then roll in dried natural breadcrumbs. Deep fry until golden.