In a greased slow cooker, whisk together the coconut milk, chicken broth, peanut butter, red curry paste, fish sauce, soy sauce, brown sugar, garlic, ginger, and red pepper flakes until smooth.

Add the chicken breasts, diced onion, red bell pepper, carrots, mushrooms, and broccoli. Stir to ensure all ingredients are submerged.

Cover and cook on high for 3-4 hours or on low for 6-8 hours, until the chicken is fully cooked and the vegetables are tender.

Remove the chicken breasts, shred with two forks, and return the shredded chicken to the soup.

Stir in lime juice, adjust seasoning with salt, and add more curry paste or red pepper flakes if desired.

Serve the soup over cooked rice or noodles and garnish with cilantro and chopped peanuts.