Place the eggs, flour and salt into the bowl of your mixer fitted with the bread blade. Mix slowly and add water as needed to the dough. Once the dough is well blended, not flaky or too wet (add more flour if this is the case) remove, place on cutting board and cover with a bowl. Let rest for 10 minutes or until ready to use.
Using the pasta machine, follow manufacturer directions to prepare long strips of pasta. I use Kitchen Aid and the last turn of pasta is with number 6. Cut them in strips 4 inches long.
In a large pan warm the olive oil and add the garlic. Cook the garlic but insure that it will not turn brown or burned. Add the meat and cook until all the meat is cooked on the outside. Cut down any chunks of meat. Add the tomatoes basil salt and pepper. Cook over medium low heat for at least 30 to 45 minutes. Taste and rectify flavor if so needed
In a large heavy bottom pan over medium heat melt butter and add the flour. With a whisk mix well until a thick cram is formed. Add slowly the milk constantly whisking making sure no lumps is formed. Add more milk as the sauce thickens. Add salt, pepper and grated nutmeg as needed. The sauce should leave a thin layer of sauce on the back of a wooden spoon when it is ready.
In a large pot with salted water and 1 tablespoon of oil cook 6 to 8 strips of pasta at the time. Cook for at least 5-7 minutes; they should be cooked, but not too tender. Remove from water with the assistance of a hand colander and place in a bowl of cold water to stop the cooking process. Repeat this process until all the pasta is cooked.
In a large baking pan cover the bottom with an even thin layer of tomatoes. Remove one at the time the past from the bowl of water, removing any excess water and place flat on the bottom of pan. Cover the bottom of pan. Add a thin layer of tomatoes sauce and spread evenly. Add a thin layer of Besciamella sauce over it, spread evenly. Add the shredded mozzarella. Cover with another layer of pasta.
Repeat the above process 1 or 2 more layer are made. When all layers are done, spread a thin layer of Besciamella, top it with tomatoes sauce. Spread remaining mozzarella on the top.
Cook in a hot oven set at 350 for 45 minutes or until the tops is golden brown and the sides are nice and bubbly.
Let it rest before serving. It can be cooked the day before, rested in the refrigerator and warmed again for 30 minutes the day after. This will allow the sauce to sip into the pasta and increase the flavor.