Season the goat meat thoroughly in a large bowl with 2 tablespoons of curry powder, salt, black pepper, garlic, onion, and ginger. For the best flavor, let it marinate in the refrigerator for at least 30 minutes, or overnight if possible.

Heat the vegetable oil in a large Dutch oven or heavy-bottomed pot over medium-high heat. Add the remaining 1 tablespoon of curry powder to the hot oil and stir constantly for about 30 seconds until it becomes highly fragrant and slightly darkened.

Add the marinated goat meat to the pot in batches, searing until the meat is browned on all sides, about 5 to 8 minutes. Return all the browned meat to the pot and pour in any remaining marinade juices.

Pour in the beef broth, ensuring the goat meat is mostly submerged, then toss in the thyme sprigs and the whole scotch bonnet pepper. Bring the liquid to a rolling boil, then immediately reduce the heat to low, cover with a tight-fitting lid, and simmer gently for 90 minutes.

Stir in the cubed potatoes and continue to simmer uncovered for an additional 25 to 30 minutes. The curry is ready when the potatoes are fork-tender and the sauce has reduced into a rich, thick, savory gravy.

Carefully remove and discard the scotch bonnet pepper and woody thyme sprigs before serving. Serve this tender curry hot over a bed of traditional Jamaican rice and peas with a side of fried plantains.