Heat olive oil in a large skillet over medium heat. Sauté chopped onion until translucent, about 5 minutes. Add minced garlic and cook for another minute.

Stir in ground beef or pork, browning for about 7-10 minutes. Add crushed tomatoes and tomato paste. Pour in red wine if using and season with salt, pepper, oregano, and basil. Simmer uncovered for 30-40 minutes.

Melt butter in a saucepan over medium heat, whisk in flour to form a roux. Gradually add milk while whisking. Cook until the béchamel thickens, about 5-7 minutes. Season with salt and nutmeg.

Cook lasagna noodles in salted boiling water until al dente, about 8-10 minutes. Drain and lay flat on a towel.

Preheat oven to 375°F (190°C). In a greased baking dish, layer meat sauce, noodles, béchamel sauce, and cheeses. Repeat layers, finishing with béchamel and cheese on top.

Cover with foil and bake for 25-30 minutes. Remove foil and bake for another 10-15 minutes until golden brown. Let rest for 10-15 minutes before slicing.