Add cubed goat meat to a large ziplock bag. Mix curry, allspice, black pepper, sea salt, paprika, ginger, and thyme then add to the same bag. Top with crushed garlic and work into the meat. Allow the flavors to infuse for 2+ hours.
Heat oil in a Dutch oven. Sear meat, in batches, if necessary. Add chopped onion, and cook until soft. Finally, stir in the tomato paste and cook for a few minutes more.
Pour chicken broth, crushed tomatoes, and coconut milk into the pot. Add dried Arbol chiles, then bring the mixture to a boil over medium heat. Reduce heat to low, then cover and simmer for 11/2 to 2 hours, or until the meat is nice and tender.
Peel and cube potatoes, then stir into the curry. Cover and continue to cook, over low heat, for an additional 30 minutes or until the potatoes are fork-tender and the sauce is thick and rich.