Pat Dry: Start by patting the lamb shoulder dry with paper towels. Season generously with salt to enhance the flavor as it cooks.
Sear the Lamb: Heat vegetable or coconut oil in a large pot over medium-high heat. Sear the lamb pieces until browned on all sides, about 5-7 minutes per batch. Set them aside when done.
Sauté Onions: In the same pot, reduce the heat to medium and add the chopped onion. Sauté for about 5 minutes until they become translucent and sweet.
Add Aromatics: Next, stir in the minced garlic, grated ginger, and fresh thyme. Cook for 1 minute, allowing the wonderful scents to blend together.
Incorporate Tomato Paste: Stir in the tomato paste and let it cook for an additional minute.
Toast Spices: Add brown sugar, ground allspice, and black pepper, stirring for 30 seconds.
Mix in Lamb and Sauce: Return the seared lamb to the pot. Pour in soy sauce along with chopped scallions and the whole Scotch bonnet pepper. Add the stock and deglaze the pot.
Bring to Boil: Let the mixture come to a boil. Once boiling, reduce the heat, cover, and let it simmer for 1 hour and 15 minutes.
Add Creaminess: Stir in the coconut milk, sweet potatoes, and carrots. Simmer gently for another 45 minutes to 1 hour, until the veggies are tender.
Final Touches: Turn off heat and carefully remove the thyme sprigs and Scotch bonnet. Squeeze in fresh lime juice, adjusting the salt to your taste before serving.