Peel onions and garlic. Peel and wash the carrots. Dice everything very finely. Heat the oil in a large pan. Fry the onions, garlic and carrots for about 1 minute. Season with salt and pepper. Add tomato paste and sauté briefly. Stir in tomatoes and oregano and simmer everything for about 5 minutes. Leave to cool.
For the béchamel sauce, heat butter in a pot. Dust with flour and sauté until light brown. Add milk and 500 ml water while stirring. Bring to the boil, stir in the stock and simmer everything for about 5 minutes while stirring. Season to taste with salt, pepper and nutmeg.
Mix minced meat and carrot mixture. Season with salt and pepper. Fill the cannelloni with the mixture and place in a greased casserole dish. Put the rest of the filling in the baking dish. Pour sauce over it. Grate cheese finely and sprinkle over it. Bake in a preheated oven (electric cooker: 200 °C/circulating air: 180 °C/gas: see manufacturer) for 30-35 minutes.