Peel the potatoes and boil them in salted water for about 15 minutes. Clean, peel and dice the carrots. Cook in boiling salted water for about 5 minutes. Drain. Peel and finely dice onion.
Whisk the egg. Wash cutlets, dab dry, season with salt and pepper and turn in the egg. Sprinkle with oat flakes all around. Heat oil in a small coated pan and fry the schnitzel in it at medium heat for about 4 minutes on each side.
Remove from the pan. Sauté the onion in the frying fat. Add 2 tablespoons of carrots and fry briefly. Drain the potatoes and mash them with a potato masher. Add milk and stir in. Add remaining carrots and fold in.
Season to taste with salt and pepper. Arrange the schnitzel, purée and onion-carrot mixture on a plate and serve garnished as desired with chive rolls, a slice of lemon and parsley.