Egg Pasta: Combine eggs and flour in mixer. Press through pasta maker to desired thickness.
Bolognese Sauce: Heat the butter and oil in a heavy sauce pan over medium heat. Add the chopped vegetables and sauté until softened. Add the ground beef and chopped meats. Cook for about 10 minutes or until the meat is fully cooked and browned bits begin to form along the bottom of the sauce pan. Add the wine to the pan and let evaporate, stirring up the browned bits. Add the tomatoes and simmer for around 30 minutes. Season to taste, add ½ cup broth. Cover and simmer another 45 minutes, adding the remaining broth if the sauce becomes too thick. Taste the sauce and add additional seasoning if needed. Add enough cream to lighten the color in the last 5 minutes of cooking. Remove from heat.
Bechamel Sauce: Melt the butter in a saucepan add the flour and cook for a minute or two. Do not let brown. Slowly add the milk, stirring constantly to prevent lumps. Continue cooking until the sauce thickens. Season with salt, white pepper and a dash of nutmeg. Set aside to cool, placing a greased piece of plastic wrap on top to prevent film from forming.
Pasta: Bring a large pot of salted water to a full boil. Cook the pasta sheets for 10 seconds only, immediately submerge in cold water. Drain.
To Prepare Lasagne: Pour in a little of the meat sauce into a 9 x 13 baking pan. Layer noodles along the bottom. Spread one layer of the meat sauce, than another layer of noodles. Spread a layer of béchamel over the noodles then sprinkle with a little of the mozzarella and parmesan cheese. Continue in the manner until all the noodles are used, topping the dish with the final layer of béchamel layer and cheese. Dot the top with butter and bake in a 375 degree oven for about 40 minutes or until bubbling and lightly browned.