Heat olive oil in a large Dutch oven over medium-high heat. Season the beef short ribs with salt and pepper. Sear the short ribs on all sides until browned, about 8-10 minutes. Remove from the pot and set aside.

Sauté Aromatics

In the same pot, add the sliced shallots and sauté until translucent, about 3-4 minutes. Add minced garlic and cook for an additional minute until fragrant.

Make the Ragu

Return the short ribs to the pot. Add the crushed tomatoes and beef broth. Bring to a simmer, then cover and reduce the heat to low. Cook for about 2-2.5 hours, or until the beef is tender and easily pulled apart.

Cook the Rigatoni

In a large pot of salted boiling water, cook the rigatoni according to package instructions until al dente. Drain and set aside.

Combine and Serve

Once the beef is tender, remove it from the pot and shred the meat. Return the shredded beef to the ragu and stir in the chopped basil. Adjust seasoning with salt and pepper. Serve the ragu over rigatoni, topped with grated Parmesan cheese and additional basil if desired.