Make a well with the flour on a large cutting board. Crack the eggs in the center of the well and season with salt.
Fold the flour into the eggs to form a dough. Knead and let rest for about 1 hour.
Roll into large sheets. Boil sheets in salted water and drain onto a rack. Reserve for assembly.
Heat the oil in a large sauce pot. Season the ribs with salt and pepper. Add the short ribs to the pot and brown on all sides.
Remove the short ribs and add the pancetta. Brown lightly then add the onions and carrots. Brown lightly then add the garlic.
When the garlic is toasted, add the wine and reduce by half. Add the basil stems and veal stock and let cook for about 20 minutes.
Add the tomatoes and let cook for 1 hour on low heat. Season with salt, pepper and chili flakes.
Warm the milk in a sauce pot. Heat the butter in another sauce pot. Add the garlic and cook for 2 minutes.
Add the flour and cook over low heat for 3-4 minutes without getting any color. Add the warm milk and let cook for 25-30 minutes.
Add the cheese and season with salt and black pepper.
Blend ricotta, eggs, pecorino, salt, and black pepper together. Season to taste.
Put a layer of meat sauce on the bottom of a casserole dish. Place a layer of pasta to cover the bottom.
Top with a layer of meat sauce then a layer of bechamel or ricotta. Sprinkle with grated cheese.
Continue with this until you have a full casserole. Top with more sauce and grated cheese and bake for 45 minutes.
Remove from the oven and let rest for at least 30 minutes or overnight. Cut into portions. Serve with extra sauce on the side and more grated cheese.