Marinate the beef with browning sauce, soy sauce, Worcestershire sauce, all-purpose seasoning, allspice, onion, garlic, ginger, and green onions for 1 hour, keeping it covered and chilled. The aromatics should cling to the beef cubes so they color as they cook.

Heat vegetable oil in a Dutch oven with brown sugar until the sugar darkens, then add the beef (reserving the aromatics) and sear for 6-8 minutes, stirring only enough to brown evenly. Look for deep browned edges on the beef.

Stir in the reserved aromatics, then mix in ketchup, beef broth, fresh thyme, and the whole scotch bonnet pepper. The liquid should turn deep brown and glossy, with thyme visible throughout.

Cover and simmer for 1 1/2 hours, maintaining gentle bubbling until the beef is nearly tender. You should see the gravy thicken slightly and the beef fibers begin to loosen.

Add carrots and potatoes, then simmer for 30-40 minutes until the vegetables are tender. The stew should keep a steady simmer with visible carrot and potato pieces.

Stir in butter beans and simmer for 10 minutes. The beans should heat through without splitting, keeping the stew hearty.

Remove the scotch bonnet and thyme stems before serving, then ladle the stew over rice. The surface should look glossy and cohesive with meat and vegetables evenly distributed.