It’s a myth that you need to boil fresh or dried lasagne noodles before baking the whole thing, but what is true is that lasagne is better the second day, when it has settled, so if you have the time, I recommend making this a day before you plan to serve it.

To make the Bolognese sauce, heat 2 tablespoons of the olive oil in a medium, heavy-bottom pot over medium-high heat. Add the onion, carrots, celery, garlic, and thyme and season with salt and pepper. Cook, stirring regularly with a wooden spoon, until the vegetables are tender and have released their juices: 7 to 9 minutes.

Stir in the livers and cook over high heat for 2 minutes, then add the beef, veal, and pork, stirring and breaking up over high heat. Season again with salt and pepper.

Continue to cook over high heat until the meat is brown, stirring regularly and scraping the bottom of the pot as necessary to keep the meat and vegetables from scorching.

Once the meat is browned, stir in the tomato paste over medium heat. Let cook for about 20 minutes, stirring regularly. Add the wine, bring to a boil, and let cook until reduced by half, then add the milk and bay leaves and bring to a boil. Reduce the heat to a simmer and cook for 1½ to 2 hours, stirring occasionally. You may need to add a bit of water (or chicken or veal stock, if you have it) if the sauce seems to require it.

Taste the sauce and season with salt and pepper if necessary. Remove from the heat and stir to release steam and allow it to cool slightly. Skim the fat off the top with a ladle and discard.

Preheat the oven to 180 degrees Celsius.

Coat the inside of a 9 x 13-inch (or similar size) baking dish with the remaining 1 tablespoon oil. Cover the bottom of the dish with a layer of béchamel. Sprinkle some Parmigiano-Reggiano cheese atop the béchamel. Top it with a layer of noodles. Top the noodles with a layer of Bolognese sauce, and repeat with the béchamel, grated cheese, noodles, and Bolognese until the pan is full to the top. The top layer should be Bolognese, dotted with béchamel, with thin slices of mozzarella laid across the top.

Place the baking dish on a sheet pan and bake in the oven for about 50 minutes, until the lasagne is browned on top and beginning to bubble. Remove from the oven and let cool. If you must serve it the day you’ve made it, let it rest for 15 minutes before slicing. For best results, let cool completely overnight. The next day, reheat, covered loosely with foil, until bubbling. Remove from the oven, let rest 20 minutes, then serve.