Trim any large pieces of excess fat from the short ribs and pat them dry with paper towel. Season generously with kosher salt on all sides.
Set your pressure cooker to the sauté setting and add the neutral oil. Once hot, sear the short ribs on all sides until deeply golden, about 2-3 minutes per side. Transfer to a plate and set aside.
Keeping the sauté setting on, add the aromatics (ginger, onion, and garlic) cut-side down into the cooker. Cook until the cut sides are nicely browned and fragrant, about 3-4 minutes. Remove and set to the side.
Add the tomato paste and gochujang to the pressure cooker. Cook for 2-3 minutes, stirring often, until the mixture darkens slightly and becomes very fragrant.
Return the charred aromatics to the pot. Add the soy sauce, rice wine vinegar, and beef broth, then nestle the seared short ribs back into the liquid.
Pressure cook on high for 45 minutes and allow a natural release of the steam, then carefully use the quick release button to release any remaining pressure before removing the lid.
Carefully remove the short ribs to a plate—they will be very tender. Discard the aromatics from the broth, then strain the broth through a fine mesh sieve into a bowl. Pour the strained broth back into the pressure cooker to keep warm.
Shred the short ribs off of the bones and loosely cover with foil to keep warm.
Meanwhile, bring a pot of water to a boil and cook the ramen noodles according to package instructions. Drain well.
Divide the noodles between bowls. Top with the shredded short rib and ladle the hot broth overtop.
Garnish with lime wedges, scallions, cilantro, sesame seeds, and a drizzle of sesame oil.