Peel and dice the parsnips and potatoes and cook in boiling salted water for about 30 minutes until soft. Drain vegetables, collect cooking water. Puree about 1/3 of the cooking water with the vegetables very finely. Puree first through a strainer (straining mill) with a fine insert, then 2x through a fine sieve, if necessary dilute with soaking water in between. Stir in double cream, season to taste with salt, pepper and a little sugar
Wash the meat, dab dry. Heat 1 tablespoon of oil in a frying pan. Fry the lamb chops for 5-6 minutes, season with salt and pepper, take them out, wrap them in foil and let them rest in a warm place for about 5 minutes.
Wash mint, shake dry. Pluck the leaves from the stalks. Heat 5 tablespoons of oil in a saucepan. Roast the mint leaves in it at medium heat for 3-4 minutes until crispy. Wrap chops out of the foil, arrange with puree on plates, sprinkle with mint oil