Peel and chop the onion and garlic. Peel, wash and finely chop the carrots. Heat the oil in a pot. Fry the minced meat in it until crumbly. Season with salt and pepper. Add onion, garlic and carrots and fry briefly.
Add tomato paste and herbs to the mince and sauté briefly. Deglaze with 1⁄2 l water and bring to the boil. Season sauce with salt, pepper and 1 pinch of sugar. Simmer everything for about 15 minutes.
Melt the butter. Peel and wash the potatoes and slice or slice them thinly. Season the minced sauce to taste and spread in an ovenproof dish. Spread the potato slices in several layers in flakes.
Season each potato layer with salt and spread with melted butter.
Grate the cheese and sprinkle on the potatoes. Bake gratin in the preheated oven (electric cooker: 200 °C/circulating air: 175 °C/gas: see manufacturer) for approx. 40 minutes until golden brown. Drink tip: dry white wine.