In a large Dutch oven or saucepan, heat the olive oil and butter. Add the onions, celery and carrots and cook until they become very soft and begin to caramelize.

In a large bowl, mix together the pancetta, veal, beef and pork. Add the meats to the pan and cook until they begin to brown.

Add the wine and continue to cook until most of the liquid is evaporated—it should just be moist around the edges of the meat.

Add the tomato paste and stir well. Reduce the heat to low and cook for 2 hours.

If making your own pasta, divide the dough into 8 portions. Roll each one out through the thinnest setting on a pasta machine and lay the sheets on a lightly floured surface to dry for 10 minutes.

Cut the pasta into 5-inch squares and cover with a damp kitchen towel.

Bring 6 quarts of water to a boil in a large pot and add 2 tablespoons salt. Set up an ice bath next to the stovetop.

Drop the pasta into the boiling water, 6 or 7 pieces at a time, and cook until tender, about 1 minute. Transfer to the ice bath to cool, then drain on kitchen towels, laying the pasta flat.

Preheat the oven to 375°F.

Assemble the lasagne in a 10-by-20-inch lasagna pan: spread a layer of Bolognese ragù over the bottom and top with a sprinkling of Parmigiano Reggiano DOP, a layer of pasta, a layer of besciamella, another layer of ragù, a sprinkling of Parmigiano Reggiano DOP and pasta. Repeat until all the ingredients are used up, finishing with a layer of pasta topped with besciamella, sauce and Parmigiano Reggiano.

Bake for 45 minutes, or until the edges are browned and the sauces are bubbling.

Allow the lasagna to stand for 10 minutes before serving.