Preheat oven to 300°.
Season short ribs generously with salt and pepper and let them come up to room temperature.
Heat cooking fat or oil in a large Dutch oven over medium-high.
Brown short ribs on all sides. Then transfer to a plate and drain off most of the fat.
Add uniformly chopped onions, carrots, and celery to pot and brown over medium-high heat, stirring often, until the onions are translucent.
Add tomato paste; cook, stirring constantly, until well combined and deep red, 2-3 minutes.
Deglaze with a touch of red wine (good enough to drink) and reduce until almost dry. Add short ribs.
Stir in stock. Bring to a simmer, cover, and transfer to oven.
Cook until short ribs are tender, 3 to 4 hours. Transfer short ribs to a platter. Strain sauce from pot into a measuring cup. Spoon fat from surface of sauce and discard; season sauce to taste with salt and pepper.
Read more about the specifics of braising here.