Pat dry the short ribs with some paper towel. Season the short ribs on all sides with salt and pepper.
Turn the Instant Pot to Saute, Normal mode, add a tablespoon or so of olive oil. Working in batches, add short ribs and brown on all sides, about 2-3 minutes per side. Add a little extra oil in between batches.
You might end up with quite a bit of rendered fat from the short ribs. Pour off some of it, you only need about 2-3 tablespoons of fat for the next step.
While still on Saute, add onions, celery and carrots. Cook for about 5-6 minutes, stirring a few times, until browned slightly.
Add the garlic cloves and stir through. Pour in the red wine and scrape the bottom of the pot. Let it cook off for a minute or so for the alcohol to evaporate partially.
After a minute or two, add the beef stock and add tomato paste. Stir well, scraping the bottom of the pot for about 2 minutes.
Return the browned short ribs to the broth, nestling them as deep as you can. Add the thyme and bay leaves.
Secure and lock the lid. Set to Pressure Cook for 45 minutes on HIGH with 15 minute natural release. Then use the quick release to let off the remaining pressure.
Open the lid. Carefully remove short ribs to a clean plate. Cover the ribs to stay warm while you reduce the sauce.
Using a slotted spoon, fish out some of the vegetables and all of the herbs and leaves.
Add the honey and turn the Instant Pot back on Saute setting, HIGH mode. Cook for 10-15 minutes or until the sauce has reduced by a third.
Whisk a tablespoon or two of the flour with ¼ cup of the cooking broth in a separate bowl until smooth slurry forms. Pour the slurry into the sauce to thicken and stir in the butter.
Pour some of the sauce over the ribs on a platter or in a bowl OR return the ribs back to the pot to stir through the sauce.
Finish with plenty of chopped parsley. Serve over mashed potatoes or creamy polenta.
