Step 1
Place a rack in middle of oven; preheat to 300°. Place 4 lb. English-style bone-in beef short ribs on a rimmed baking sheet, pat dry, and sprinkle all over with 1 Tbsp. Diamond Crystal or 1¾ tsp. Morton kosher salt and 2 tsp. freshly ground pepper. Heat 2 Tbsp. vegetable oil in a large ovenproof Dutch oven or other heavy pot over medium-high. Working in batches if needed, cook short ribs on all 4 sides until a deeply browned crust forms, about 3 minutes per side. Transfer to a plate with tongs. Carefully pour fat into a small bowl. Return 2 Tbsp. fat to pot; discard the rest.
Step 2
Cook 2 large white onions, coarsely chopped, 2 large carrots, peeled, coarsely chopped, 4 celery stalks, coarsely chopped, and 10 garlic cloves, coarsely chopped, in same pot, stirring often, until softened and starting to brown, 10–14 minutes. Sprinkle ¼ cup (31 g) all-purpose flour over; stir until vegetables are evenly coated, then gradually pour in 1¼ cups bourbon, 3 Tbsp. Worcestershire sauce, 2 Tbsp. red wine vinegar, and 6 cups water, stirring constantly to combine. Add 4 dried bay leaves, ⅓ cup (67 g; packed) dark brown sugar, 3 Tbsp. instant espresso powder, 2 tsp. Diamond Crystal or 1¼ tsp. Morton kosher salt, and 1 tsp. freshly ground pepper and bring to a boil. Immediately remove pot from heat; nestle ribs into sauce so they are mostly submerged. Cover pot, transfer to oven, and braise until meat is tender, about 3 hours. Uncover and roast until sauce thickens slightly and tops of ribs are browned, 25–35 minutes.
Step 3
Using a slotted spoon, carefully transfer short ribs to a
clean plate. Strain sauce through a fine-mesh sieve into a small bowl; discard solids.
Skim fat from surface, then taste and season with more salt if needed.
Step 4
Serve short ribs over mashed potatoes if desired with sauce poured over and seasoned with more pepper.
Do ahead: Ribs can be cooked 2 days ahead. Let cool; cover and chill. Skim fat from surface before reheating, covered, in a 300° oven, 20–30 minutes.