To make this dish, start by preheating your oven to 350°F. Pat the short ribs very dry, then coat them well in the flour, making sure all sides are evenly covered.
Set a large Dutch oven over high heat and add the avocado oil. Once the oil is very hot and shimmering, add the short ribs and sear them on all sides for about 2–3 minutes per side, until deeply browned. Remove the ribs from the pot and set them aside.
In the same pot, add the diced onion, carrots, celery, and peeled garlic. Stir in the Dijon mustard and tomato paste, then pour in the red wine and beef broth, scraping up all the browned bits from the bottom of the pot as you mix. Add the peppercorns and brown sugar, stir well, and bring the mixture to a gentle boil.
Once the liquid is bubbling, return the short ribs to the pot and nestle in the rosemary sprigs. Cover the Dutch oven, then transfer it to the oven and let the ribs braise for 3 hours, until the meat is extremely tender and easily falls off the bone.
Remove the pot from the oven and discard the rosemary.
At this point, you have two options: serve the short ribs directly with the vegetables and sauce from the pot, or strain everything and reduce the sauce over medium heat by about half, which will take 20–22 minutes, then spoon it over the ribs.