Makes 1 (9-by 13-inch) casserole
Make Bolognese Sauce:
Place onion, garlic, carrots and celery in the bowl of a food processor. Pulse until finely chopped, scraping down the sides of the bowl once or twice. Heat olive oil and butter in a large pot over medium-high heat. Add onion mixture and cook, stirring occasionally, until tender, about 10 minutes. Add beef, veal and pancetta and cook, breaking apart the meat, until no longer pink. Stir in tomato paste, milk, wine and tomatoes and bring to a boil. Reduce to a gentle simmer and cook, stirring occasionally, until the sauce has thickened, 1 to 1½ hours. Season well with salt and pepper. Sauce can be made up to 2 days ahead. Cover and chill until ready to use. Warm gently in a saucepan before assembling lasagna.
Make the Béchamel Sauce:
In a medium saucepan, melt butter over high heat. Add flour and cook, whisking constantly, until roux is golden brown, 1 minute. Add milk and continue whisking until milk begins to boil and thickens enough to coat the back of a spoon. Remove from heat, and season with salt and pepper; set aside. Béchamel can be made 1 day ahead. Cover and chill until ready to use. Warm gently in a saucepan before assembling lasagna.
Cook the Pasta:
Follow the package instructions for par-boiling lasagna pasta, or purchase no-boil lasagna. Set cooked noodles aside until ready to assemble.
To Assemble the Lasagna:
Preheat oven to 350°. Spoon a thin layer of the meat sauce into the bottom of a 9-by 13-inch baking dish. Then, layer with lasagna sheets, ½ cup of the béchamel sauce, 1 cup of the meat sauce and ¼ cup of Parmesan. Repeat the layers 4 more times. Top with remaining ½ cup Parmesan. Cover loosely with foil and bake until bubbling, about 45 minutes. Remove foil and continue to bake until cheese begins to brown, 10—15 minutes. Let stand 15 minutes before slicing.