Peel, wash and finely dice the carrot. Peel and finely dice onion and garlic. Heat the oil in a frying pan. Fry the onion, garlic and carrot over medium heat for about 10 minutes.
Add the mince and fry over a high heat until the liquid has evaporated. Chop the tomatoes in the tin with a knife and add to the mince with the bay leaf. Stir in tomato paste. Season with salt, pepper and sugar and cook over medium heat for about 30 minutes, stirring occasionally.
In the meantime cut the bread into 8-12 slices. Spread out the slices on a baking tray and roast in a preheated oven (electric cooker: 225 °C/ convection oven: 200 °C/ gas: level 4) for approx. 6 minutes until golden brown. Take them out and let them cool down on a grid.
Reduce oven temperature (electric cooker: 200 °C/ circulating air: 175 °C/ gas: level 3). Wash oregano, dab dry, pluck leaves from the stalks and chop finely. Melt the fat in a pot. Add flour and sweat for about 3 minutes.
Deglaze with stock and milk, bring to the boil and simmer while stirring for about 5 minutes. Season with salt, pepper and nutmeg and remove from heat. Drain mozzarella and cut into slices. Stir the chopped oregano into the bolognese.
Grease an ovenproof casserole dish (1 litre capacity). Spread 1/4 of the Bolognese sauce on the bottom. Spread half of the slices of bread on it and pour half of the béchamel sauce over it, then spread half of the bolognese sauce on top.
Spread the rest of the bread loosely and spread the rest of the Bolognese and béchamel sauce between the slices. Finish with mozzarella, not covering the bread completely. Bake the lasagne in a preheated oven (electric cooker: 200 °C/ convection oven: 175 °C/ gas: level 3) for about 30 minutes.
Take out and let it cool down a little. Serve garnished with oregano.