Step 1
Place a rack in center of oven; preheat to 350°. Sprinkle one 4-lb. boneless beef chuck roast throughout with 2 Tbsp. Diamond Crystal or 1 Tbsp. plus ½ tsp. Morton kosher salt and 2 tsp. freshly floor pepper. Warmth ¼ cup vegetable oil in a big ovenproof Dutch oven or different heavy pot over medium-high. Cook dinner roast, turning often, till browned throughout, 15–20 minutes. Switch to a big plate.
Step 2
Scale back warmth to medium and prepare dinner 2 small onions, finely chopped, and 2 small celery stalks, finely chopped, in similar pot, stirring usually and scraping up browned bits caught to backside, till golden brown and softened, 9–13 minutes. Add 10 garlic cloves, finely chopped, and one 3″ piece ginger, peeled, finely chopped, and prepare dinner, stirring usually, till aromatic, 2–3 minutes. Add 2 Tbsp. all-purpose flour and prepare dinner, stirring consistently, till mixed, about 2 minutes. Regularly pour in ⅔ cup darkish rum, stirring consistently to stop clumping, then add 2½ cups low-sodium beef broth, 2 cups ginger beer, 3 Tbsp. recent lime juice, 3 Tbsp. Worcestershire sauce, and 1 Tbsp. gentle brown sugar. Improve warmth to excessive and convey to a boil. Cook dinner, stirring often, till sauce is lowered by about one third and thick sufficient to flippantly coat a spoon (it needs to be the consistency of heavy cream), 15–20 minutes. Style sauce and season with extra salt and pepper if wanted.
Step 3
Take away pot from warmth and place roast in middle of pot. Organize 1 lb. carrots, peeled, reduce into 1″ items, and 1 lb. small yellow potatoes (15–20), scrubbed, round meat, cowl, and braise in oven till meat is tender sufficient to shred within the middle with out a lot resistance, 3–3½ hours. Uncover and switch meat over. Roast till meat is browned on high and sauce thickens barely, 30–45 minutes. (If roast is browning too shortly, flip over and proceed roasting till sauce thickens.) Skim as a lot fats from floor as attainable; discard. High with mint and/or cilantro leaves with tender stems (if utilizing) and serve with lime wedges for squeezing over if desired.
Do forward: Roast will be cooked 3 days forward. Let cool; cowl and chill. Skim fats from floor earlier than reheating, coated, in a 350° oven, 20–half-hour.