Season short ribs generously with salt and pepper.
Turn on sauté setting on pressure cooker. Once hot, add 2 tablespoons of olive oil and sear short ribs on all sides (except bone side). Do this in a few batches. If you put too many in the cooker at once, it will not stay hot enough to sear them well. You really want a lot of color on them, so take your time. This took me about 15-20 minutes, but it's worth it. Otherwise, your meat will be gray and look sad.
After done searing all the meat, DO NOT clean out the bottom! You want all that flavor to go into your sauce. Add the tomato paste directly to the pot and mix around for about 30 seconds. This is called "cooking out" the paste. It really needs this step since it's been sitting in a can for who knows how long.
Add wine, onions, garlic, thyme, and rosemary. Bring it up to a boil and let cook for at least 5 minutes, gently scraping up all the brown bits from the bottom of the pot.
Add beef stock to pot and carefully place short ribs in the sauce. They should be about 3/4 covered in sauce, but not submerged. Set manual timer for 40 minutes at high pressure. Once cook time is complete, allow pressure to release naturally.
After short ribs are finished cooking, carefully remove them to a serving (or holding) dish. Pour remaining sauce through a fine mesh strainer into a large bowl. Skim off as much of the fat as possible to make the most appealing sauce to pour over your short ribs, mushrooms, and bacon.