Begin by removing the sausage meat from its casing and transfer it to a bowl. Use a fork to roughly mash the meat. Finely chop the onions, celery, and carrots.

In a large saucepan, heat the oil over low heat. Add the chopped vegetables and let them cook for about 10 minutes, until softened.

Add the sausage meat to the saucepan and brown it evenly. Pour in the wine and continue to cook on low heat for at least two hours, stirring occasionally. If the ragù becomes too dry during cooking, add a ladleful of vegetable stock as needed.

About 15 minutes before the ragù finishes cooking, clean and slice the mushrooms. Add them to the meat mixture, stirring well. Add more stock if necessary, and season lightly if needed, keeping in mind that the sausage meat is already quite savoury. Once cooked, cover the ragù and set aside in a warm place.

To prepare the béchamel sauce, melt the butter in a saucepan over low heat. Add the flour and stir well. Continue cooking for a couple of minutes, stirring constantly. Gradually add the milk, making sure to incorporate it well into the roux before adding more. Once all the milk has been added, increase the heat to medium and stir until the sauce has thickened. Season with a pinch of salt, pepper, and nutmeg. Cover the béchamel and set aside in a warm place.

To prepare the lasagne sheets, cook them in boiling salted water, despite package instructions that may say otherwise. Cook for about 9 minutes for dried lasagne and 2 minutes for fresh lasagne. This ensures the pasta is thoroughly cooked, as the sauce may not be watery enough to cook the sheets properly. Be cautious not to overlap the cooked lasagne sheets, as they may stick together and become difficult to handle.

Preheat the oven to 170˚C (340°F)/ gas mark 3. Choose an oven-safe dish measuring approximately 30cm x 23cm (12″ x 9″). Begin by spreading a thin layer of béchamel sauce over the bottom of the dish. 

Next, place a layer of lasagne sheets on top of the sauce, followed by an even layer of the prepared ragù. Drizzle additional béchamel sauce over the ragù, and then sprinkle with a layer of the mixed grated Parmesan and Pecorino cheese.

Continue layering in this sequence—lasagne sheets, ragù, béchamel, and grated cheese—until you have used all the ingredients. Finish with a final layer of lasagne sheets, topped with béchamel and a generous amount of grated cheese.

Place the assembled lasagna in the preheated oven and bake for 45 minutes. Cover the dish with aluminium foil for the first 30 minutes to prevent over-browning, and then remove the foil for the last 15 minutes to create a crispy, golden top.

After taking the lasagna out of the oven, allow it to rest for 20-30 minutes to help it set and cool slightly. This will make it easier to cut and serve.