Preheat oven to 325°F. Dry the short ribs and season generously with salt and pepper. Evenly coat the seasoned ribs with the flour.
Heat two tbsp vegetable oil in a dutch oven on high for 5 minutes. In batches brown the ribs on all sides. Remove ribs from dutch oven and set aside on a large plate or bowl.
Lower heat to medium-high. Add the last two tbsp vegetable oil to the dutch oven. Add in the onion and shallots, saute for 2 minutes. Add in the carrots, celery, and smashed garlic. Saute for another 3-4 minutes.
Add the two tbsp tomato paste, mix in and saute until all veggies are coated with it. Carefully add in the red wine and scrape the bottom of the pot making sure to get all the browned bits off the bottom. Simmer the wine until reduced by half.
While wine is reducing prepare the bouquet garni. Lay down a square piece of cheesecloth. Place the bay leaf, rosemary, thyme, and 2 sprigs parsley down in the middle of the square. Bring the corners of the cheesecloth together to create a pouch and tie it closed with some kitchen twine.
After wine has reduced add in the crushed tomatoes, beef broth, and bouquet garni. Return the ribs and any juices that were released to the dutch oven making sure to evenly disperse them. Bring the liquid to a hard simmer.
Place lid on dutch oven and transfer to preheated oven. Cook until ribs are tender, about 3 hours.
After ribs are tender, place the dutch oven on the stove. Remove the ribs and set aside on a large plate or sheet tray. Heat the dutch oven over medium heat and simmer to thicken sauce just a little. When the short ribs cool down enough, remove the meat from the bones and shred into smaller pieces.
Discard the bouquet garni from the dutch oven and spoon the grease off the top of the sauce. Return the shredded short rib meat to the dutch oven, simmer and reduce by half. Salt and pepper to taste.
Bring a large pot of well salted water to a boil. Add in pasta and cook until al dente. Drain the pasta and serve with the ragu. Garnish with parsley and shaved Pecorino Romano.