Peel and wash the potatoes and carrots. Cut carrots into slices, halve potatoes. Cook vegetables in 1/2 litre boiling salted water for 15-20 minutes. Drain vegetables, collect 1/4 litre of liquid.
Melt the fat in a pot and sauté the flour in it. Deglaze with vegetable water and milk while stirring, stir in broth. Simmer for about 5 minutes. Wash parsley, dab dry and chop finely except for a little bit for garnishing.
Add the potatoes, carrots and chopped parsley to the sauce and warm it up. Heat the oil in a coated pan. Fry the escalopes in it from both sides for about 5 minutes. Season with salt and pepper.
Season vegetables with salt and pepper. Arrange cutlets with vegetables on plates and garnish with parsley.