Preheat the oven to 300°F (150°C). Season the beef short ribs with salt and pepper. In a large Dutch oven, heat olive oil over medium-high heat. Sear the short ribs on all sides until browned, about 8-10 minutes. Remove and set aside.

Sauté the Vegetables

In the same pot, add carrots, celery, onion, and garlic. Sauté until softened, about 5 minutes.

Build the Ragù

Deglaze the pot with red wine, scraping up any browned bits. Let it reduce by half, then add beef broth, bay leaves, and thyme. Return short ribs to the pot. Bring to a simmer.

Braise the Ribs

Cover the pot and transfer to the preheated oven. Braise for 6 hours, until the meat is tender and falling off the bone.

Cook the Pasta

About 30 minutes before the ribs are done, cook the pappardelle in a large pot of salted boiling water according to package instructions. Drain and set aside.

Prepare the Mornay Sauce

In a saucepan, prepare the mornay cheese sauce. Keep warm.

Combine and Serve

Remove the short ribs from the pot and shred the meat. Discard bones and bay leaves. In a large mixing bowl, combine the pappardelle, shredded short ribs, and some of the ragù. Serve topped with mornay sauce, caramelized shallots, grated parmigiano-reggiano, and fresh herbs.