Preheat the oven to 325°F (160°C). Season the short ribs generously with salt and pepper.
In a large Dutch oven or oven-safe pot, heat the olive oil over medium-high heat. Add the short ribs and cook until browned on all sides, about 8 minutes. Remove the short ribs from the pot and set aside.
In the same pot, add the chopped onion, carrots, celery, and minced garlic. Cook, stirring occasionally, until the vegetables are softened, about 5 minutes.
Pour in the red wine, scraping the bottom of the pot to loosen any browned bits. Simmer for 3-4 minutes until slightly reduced.
Return the short ribs to the pot. Add the beef broth, crushed tomatoes, tomato paste, dried oregano, and dried basil. Season with salt and pepper to taste.
Bring the mixture to a simmer, then cover the pot and transfer it to the preheated oven. Cook for 2.5 to 3 hours, or until the short ribs are tender and falling off the bone.
Meanwhile, cook the pasta according to the package instructions until al dente. Drain the pasta, reserving a cup of pasta water.