Get short ribs with lower amounts of fat. Pat the surface of the short ribs until dry. Season with salt and pepper.
Set the instant pot to sauté on high and heat oil in the pot. Sear the short ribs on each side for 1-2 minutes. Remove the short ribs and set them aside.
Dice the onion and carrot. Add them to the pot that you seared the ribs in. Crush the garlic cloves and add them to the pot. Sauté until the onions are soft and translucent.
Add the tomato paste to the bottom of the pot and let heat for 30 seconds to a minute, then incorporate into the rest of the mixture. Sauté for another couple minutes.
Deglaze the pot with the red wine. Add the crushed tomatoes, broth, mustard, thyme, rosemary, and bay leaves to the pot and mix together.
Add back the ribs and make sure they are covered in the pot. Cover the instant pot and set to meat/stew option on high for 35 minutes.
In another pot, bring 4 cups of salted water to a boil. Add in the noodles and cook uncovered for 5-6 minutes.
Once the pressure releases from the instant pot, remove the short ribs and herbs from the pot. Simmer the sauce on low for 10-15 minutes.
Shred the short ribs and remove any overly fatty areas. Incorporate back into the sauce.
Serve the Ragu over the noodles and top with shaved parmesan and roughly chopped parsley.