Place the chicken chunks, coconut milk, red curry paste, diced onion, minced garlic, and grated ginger into the slow cooker. Stir to coat the chicken evenly with the sauce base.
Cover and cook on low for 5 hours until the chicken is fully tender.
Add the broccoli florets, bell pepper strips, salt, and black pepper to the slow cooker. Stir gently to combine.
Continue cooking on low for 1 more hour until the vegetables are tender but still hold their shape.
Stir in the lime juice right before serving. Top each portion with chopped cilantro.