Build the base: Add onion, garlic, and ginger to the slow cooker. Stir in curry paste, curry powder, turmeric, and cumin until the aromatics are coated.
Add the protein: Place chicken pieces (or chickpeas) on top.
Sprinkle with a pinch of salt to season early.
Layer the vegetables: Add bell pepper, carrots, and potatoes (or cauliflower). Cut vegetables into even pieces so everything cooks at the same pace.
Make the sauce: In a bowl, whisk coconut milk, broth, tomato paste, soy sauce, and brown sugar. Pour over everything in the slow cooker.
Set and cook: Cover and cook on Low for 6–7 hours or High for 3–4 hours, until the chicken is tender and the vegetables are soft.
Finish with brightness: Stir in lime juice.
Taste and adjust seasoning—add more salt, a splash of soy sauce, or a pinch of sugar as needed.
Thicken, if needed: For a thicker sauce, remove the lid for the last 20–30 minutes, or stir in a slurry of 1 tablespoon cornstarch mixed with 2 tablespoons cold water and cook 10 more minutes.
Serve: Spoon over rice or with naan. Top with chopped cilantro and a squeeze of lime.