Season the short ribs generously with salt and pepper from all sides.
In a large Dutch oven, heat the olive oil over medium-high heat. Add the short ribs and sear on all sides until browned, about 4-5 minutes per side. Remove the short ribs and set aside. Drain the fat, leaving about 2 teaspoons in total in the dutch oven.
In the same pot, add the onion, carrots, and celery. Cook over medium heat until the vegetables begin to soften, about 5 minutes.
Add the garlic and tomato paste and cook for another minute until the garlic is fragrant.
Pour in the red wine to deglaze the pot, scraping up any browned bits from the bottom. Cook for 2 minutes.
Add the tomatoes, bay leaves, thyme, and rosemary and pour in the beef broth.
Return the short ribs to the pot. Bring the mixture to a simmer, then reduce the heat to low. Cover the pot and let it simmer for about 2-3 hours, or until the short ribs are very tender. Uncover and cook for the last 30 minutes to allow the sauce to reduce.
Occasionally, skim off any excess fat from the surface and stir the ragu. Once the short ribs are tender, remove them from the pot and shred the meat with 2 forks, discarding the bones and any excess fat. Also remove the bay leaves and herb stems from the sauce at this time.
Optional: To the sauce, add a splash of half and half or heavy cream, and a couple of tablespoons of grated parmesan and stir. Adjust the seasoning with salt and pepper to taste.
Return the shredded meat to the pot and stir into the sauce. If the sauce is too thick, you can thin it with a little more broth.
In a large pot of salted boiling water, cook the pappardelle according to the package instructions until al dente. Drain the pasta and toss it with a bit of the ragu to coat or add it directly to the ragu and gently toss.
Serve the pappardelle with a generous amount of the short rib beef ragu on top. Grate fresh Parmesan cheese over each serving and garnish with chopped parsley.