Heat the oil over medium heat in a large skillet or saucepan. Add the shallot and ginger and sauté until tender, about 4 minutes. Add the garlic and sauté for another 30 seconds, or until aromatic.
Stir in the curry powder, brown sugar, red pepper flakes, and black pepper. Cook, stirring often, until fully combined and very aromatic, about 30 seconds.
Pour in the broth/stock and then the coconut milk and fish sauce. Bring to a boil and then turn down the heat and simmer for a few minutes.
Place the chicken, carrots, and sweet potatoes in your slow-cooker. Carefully pour the sauce over the top. Cover and cook on LOW for 5 hours or on HIGH for 2½ hours, or until chicken is very tender and fully cooked. Taste and add salt, to taste (usually 1 to 2 tsp).
In a small bowl, add 2 tbsp of cool water to the cornstarch. Use a spoon to stir the mixture until dissolved. Slowly stir in the slurry until the sauce thickens somewhat, after 1 to 2 minutes.
Serve over steamed rice and garnish with basil strips (if using).
