Prep the base: Add the chopped onion, garlic, ginger, bell pepper, and sweet potato to the slow cooker. Sprinkle with 1 teaspoon salt and black pepper.
This layer flavors the sauce and keeps the chicken from sticking.
Mix the sauce: In a bowl, whisk coconut milk, curry paste or curry powder, turmeric, cumin, brown sugar, and drained tomatoes. Add crushed red pepper if you like heat. Taste and adjust the salt if needed; the sauce should be slightly salty to season the chicken.
Add the chicken: Nestle the chicken thighs into the slow cooker and pour the sauce over the top.
Stir gently to coat everything. If it looks too thick, add a splash (2–4 tablespoons) of broth or water.
Cook low and slow: Cover and cook on Low for 5–6 hours or on High for 2.5–3.5 hours. The chicken should be tender and easy to shred or cut with a spoon.
Finish with acid: Stir in the lime juice and taste.
Add more salt, lime, or a pinch of sugar to balance. If the sauce is too thin, remove the lid and cook on High for 15–20 minutes to reduce, or mash a few sweet potato cubes into the sauce to thicken.
Serve: Spoon the curry over rice or quinoa, or serve with naan. Top with chopped cilantro.
Add a squeeze of lime at the table for a fresh finish.