Trim ribs of excess fat — a little is fine, a lot is not.
Oil lightly, then season liberally with salt and pepper.
Use the browning setting on your pressure cooker and brown ribs on all sides. You'll probably need to do this in a couple batches so you don't overcrowd. Set them aside.
To about a tablespoon of the remaining grease in the pot, add the onion and carrot and cook until just beginning to soften, about 3–5 minutes.
Add garlic and cook about a minute, then stir in the tomato paste and cook about a minute.
Sprinkle with flour, stir well to mix in, then add the paprika and mix well.
Pour in the beef broth and wine. Bring to a simmer for 5 minutes.
Add the soy sauce, then return the short ribs to the cooker with their juices. Top with thyme.
Put on the lid and set it to high pressure for 45 minutes.
When done, let the pressure release naturally.
Turn the cooker to simmer, remove the beef, shred it, return to the pot and let simmer 5 to 10 minutes or until just slightly thickened.
Serve on pasta, topped with some Parmesan cheese and a little parsley.