Peel or clean the vegetables, including the garlic and onion, and dice.
Heat the oil and fry the vegetables on a medium heat for around 10 minutes, until they start to turn brown, then remove them from the heat.
Fry the minced meat in the same pan, add salt and pepper.
Add the vegetables, along with the canned tomato slices and tomato purée. Add salt, pepper, and oregano to taste.
Simmer over a low heat for approx. 30 minutes, stirring occasionally.
Put the butter in a small pot and place over a low heat until the butter dissolves. Add the flour and whisk the mixture until smooth.
Gradually add the milk, stirring constantly, until it thickens into a sauce.
Season with nutmeg, salt, and pepper.
Bring the sauce to the boil, then remove from the heat.
Pour some of the béchamel sauce into a casserole dish, then lay the first sheet of the lasagne pasta on top. Add several tablespoons of the tomato sauce with the meat on top of the sheet of pasta.
Continue adding more layers in the same order. Sprinkle the top with grated parmesan and mozzarella.
Place the lasagne in an oven preheated to 180°C. Bake for approx. 30 minutes. When the cheese turns brown, take the lasagne out of the oven, allow it to cool slightly, and divide.