Skin the potatoes while still hot and roll in the breadcrumbs and parmesan mixed together. Dip in the beaten egg and roll the potatoes in the breadcrumb mix again. Heat the oil to 350F/180C and deep-fry for 5-6 minutes until golden. Drain on absorbent kitchen paper and keep warm.
Melt the butter, cook the garlic until golden, season, mix in the parsley and pour over the potatoes.