This dish has a special place in my heart from my childhood. The layers of flavor and care make it a dish your family and friends will remember and repeatedly request. Don't be intimidated by the long cooking time—the work can be spread out over a couple of days. This is the best and last lasagna recipe you'll ever need.
Ragù: Peel and finely mince the carrot. (Optional: use a Japanese mandoline to make thin, even slices before mincing.) Peel and finely mince the red onion. Finely mince the celery rib. Together, these ingredients make up the soffritto base of the ragù.
Warm the olive oil and butter in a large (6-quart) saucepan over medium-low heat. Add the carrot, celery and onion. Gently cook the soffritto until it is deeply browned, about 15–20 minutes. (This may take up to 45 minutes!)Mince the pancetta. Remove the sausage from its casing; add the pancetta, sausage, and ground veal to the saucepan. Increase the heat to medium, break up the sausage and veal with a wooden spoon, and cook until the meats are evenly browned and beginning to stick to the bottom of the pan, about 10–15 minutes.Add the wine and cook until it has reduced completely, making sure you scrape up anything stuck to the bottom of the pan. Add the tomato and bring the sauce to a gentle simmer. Lower the heat and simmer the sauce for at least 3 hours, until the flavors meld and the meats are completely tender. Add stock or water, as needed, if the sauce begins to dry out and stick to the bottom of the pot.
Pasta: While the ragù simmers, make the pasta sheets and bechamel sauce. (We recommend these handmade pasta sheets, but the lasagna is still very delicious with store-bought noodles.) On a wooden cutting board or clean kitchen counter, combine the two flours and a pinch of salt. Make a well in the center and add the egg yolks and whole egg. Whisk together gently with a fork, then slowly cut the dry ingredients into the wet mixture. Add the olive oil and some water, if necessary, to the well. Working from the center, continue until all the wet ingredients have been incorporated into the dough. (There may be some extra flour that can be discarded, depending on the consistency of the wet ingredients.) After the dough has come together into a mass, knead until it is shiny and uniform in texture, about 5–7 minutes. Kneading activates the gluten and gives the pasta a silky, firm bite. Wrap the dough in plastic wrap and allow it to rest for at least 1 hour, until you are ready to roll your pasta. (The pasta dough can be made several days in advance, and kept in the refrigerator.)
After the dough has rested, remove the plastic wrap and temper the dough with a rolling pin or your hands. Using a pasta maker, roll the dough out several times on the thickest setting. Adjust the setting to a medium thickness; continue rolling on increasingly thinner settings until the pasta is medium-thin in thickness. (If the thinnest setting on your machine is 9, roll it to 7; if the thinnest setting on your machine is 1, roll it to 3.) Check the thickness of the pasta by blanching a small piece in boiling water. Trim the sheets into 5" x 10" rectangles and dust lightly with all-purpose or semolina flour, to prevent sticking. Cover with plastic wrap and set aside until ready to blanch.
The quicker alternative method for pasta sheets: In a standing mixer fitted with a paddle attachment, combine the flours and salt, make a well in the dry ingredients, add the whole egg and egg yolks, and slowly work the dough with the mixer. Add the olive oil and water, if necessary, and slowly knead the dough with the paddle. Once the dry ingredients are fully incorporated, continue to knead the dough with the paddle, 1–2 minutes. Wrap and rest in the same manner as the above.
Fill a large stock pot with water, season with a generous cup of salt and bring to a rolling boil over high heat. Prepare a large bowl with ice water. With a large slotted spoon or mesh strainer, gently lower the pasta sheets, one at a time, into the boiling water. Blanch the sheets for about 45 seconds, until cooked to al dente. Place each sheet of pasta in the ice water. Spread out wax paper or plastic wrap and brush lightly with oil. Once the pasta has cooled completely, remove the pasta from the ice water, gently pat dry and spread onto the prepared wax paper or plastic wrap. The pasta sheets can be refrigerated for up to 4 hours.
Bechamel: Heat a medium (4-quart) saucepan over low heat. Melt the butter. Add the flour and mix until the flour is evenly absorbed. Continue to stir and cook until the flour begins to thicken and bind with the butter, about 1–2 minutes. Using a whisk, add the cold milk, a little at a time, until all of it has been incorporated. Bring to a simmer, lower the heat, and cook until the sauce is smooth and thick enough to thoroughly coat the back of a spoon, about 10 minutes. The bechamel sauce can be made several days in advance and kept in the refrigerator.
After about 3 hours, check the ragù sauce and season with salt and freshly ground black pepper as necessary. Have the bechamel sauce warm and easily spreadable, and the pasta sheets in easy reach. Preheat the oven to 350 degrees F. In a medium (7" x 11") baking dish or lasagna pan, spread a small amount of bechamel on the bottom. Gently lay a sheet of pasta on top. Spread about a quarter of the ragù sauce on the pasta. Add another sheet of pasta, another layer of bechamel sauce, a sprinkle of Parmesan, and another quarter of the ragù sauce. Repeat the order of the layers, finishing with a layer of pasta spread with bechamel sauce and sprinkled with Parmesan. (The assembled, unbaked lasagna can be made in advance and either refrigerated or frozen, until ready to bake.) Cover with foil and bake for about 45 minutes. Remove the foil and bake for an additional 10 minutes to allow the top to brown and bubble. Remove the lasagna from the oven, and let it rest briefly before serving.