Make the Bolognese sauce: Sauté the prosciutto and pancetta in a Dutch oven. Add the onion, carrots, celery, and garlic and cook until softened. Add the ground beef and veal and cook until browned. Stir in the tomato paste and cook until caramelized. Deglaze with the red wine, then add the beef broth and milk. Simmer for 3 hours, stirring occasionally, until thickened.
Make the pasta dough: Mix the flour and eggs until a dough forms. Knead for 5 minutes, then let rest for 30 minutes. Knead again for 5 minutes. Shape into a ball, wrap in plastic, and refrigerate overnight.
Make the béchamel sauce: Melt the butter in a saucepan. Add the shallot, garlic, thyme, and bay leaf. Whisk in the flour to make a roux. Slowly whisk in the milk and Parmesan rind. Simmer for 5 minutes until thickened. Strain and refrigerate overnight.
Roll out the pasta dough into 8.5x4.5 inch sheets. Boil the sheets for 30 seconds, then blot dry and layer in a 9x5 inch loaf pan, alternating with layers of béchamel, Bolognese, and Parmesan.
Bake the lasagna at 350°F for 1 hour, covered. Increase heat to 425°F, top with more Bolognese, and bake for 20-30 minutes until browned and bubbly. Let rest for 1 hour before serving.
