Season the short ribs generously with salt and pepper.
In a 6 or 8 quart Instant pot, press the saute function to heat up the pot. Once hot, add oil.
Sear beef, about 5-7 minutes per side, in batches if necessary. Remove beef and set aside.
Add shallots, garlic, carrots, rosemary to the pot and cook, stirring occasionally, until beginning to soften, about 3 minutes.
Add red wine, beef broth to the pot and scrape up and browned bits from the bottom to deglaze the pan. Shut off the saute function. Return the beef to the pot and cook on high pressure for 40 minutes.
When finished, use the natural release for 10 minutes and then use the quick release function to release the remaining pressure.
Once the pin has dropped, open the pressure cooker and remove the meat from the pot and set aside. If there is a large amount of fat sitting on top of the liquid, skim off and discard (see note).
Add balsamic vinegar and coconut sugar (if using) and turn on the saute function to reduce the liquid for 10 minutes.
If you want to thicken up the sauce: add 2 teaspoons arrowroot to a small bowl. Take out 2 tablespoons of the sauce from the pot and whisk it in the arrowroot to make a slurry. Pour the slurry back in to the pot and continue to boil for 1 minute.
Return meat to the pot and let cool briefly.
Serve with cauli-mash (recipe below).