Preheat oven to 350°.
Season short ribs with salt and pepper.
Heat oil in a large Dutch oven over medium-high.
Working in 2 batches, brown short ribs on all sides, about 8 minutes per batch.
Transfer short ribs to a plate.
Pour off all but 3 Tbsp. drippings from pot.
Add onions, carrots, and celery to pot and cook over medium-high heat, stirring often, until onions are browned, about 5 minutes.
Add flour and tomato paste; cook, stirring constantly, until well combined and deep red, 2–3 minutes.
Stir in wine, then add short ribs with any accumulated juices.
Bring to a boil; lower heat to medium and simmer until wine is reduced by half, about 25 minutes.
Add all herbs to pot along with garlic.
Stir in stock.
Bring to a boil, cover, and transfer to oven.
Cook until short ribs are tender, 2–2½ 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.
Serve in shallow bowls over mashed potatoes with sauce spooned over.
