Preheat oven to 300. Pat the short ribs dry and liberally salt and pepper all sides.
Heat a drizzle of olive oil in a large Dutch oven or oven safe pot over medium heat. Working in batches, sear short ribs until evenly browned on all sides, 4-5 minutes per side. Remove short ribs from the pot.
Add another drizzle of olive oil to the pot. Saute garlic and onions over medium heat until fragrant and slightly softened, 2-4 minutes. Add wine and beef broth and use a spatula to scrape up all the bits stuck to the bottom of the pan. Add short ribs back into the pot, nestling them down into the liquid, along with the herbs, and cover.
Move the pot to the oven and cook until short ribs are tender and falling of the bone, about 4 hours. Once cooked, allow the short ribs to cool completely (or overnight in the fridge) before shredding.
Once cooled, pull the short rib meat from the bones and remove the onion quarters from the liquid. Reserve about a cup of the cooking liquid for making a sauce for the pasta.
Finely dice the cooked onion quarters. Use two forks to shred the short rib meat. Depending on how you want your filling, you can leave the meat shredded like this or pulse it in the food processor a few times to break it down even more. Mix it with the diced onion. This will be your pasta filling.