Whisk together coconut milk, broth, peanut butter, curry paste, fish sauce, soy sauce, brown sugar, garlic, ginger, and red pepper flakes in greased crockpot or one fitted with a liner.
Add in chicken breasts, onion, carrots, pepper, mushrooms, and broccoli. Stir to combine.
Cover and cook on HIGH for 3-4 hours or LOW 6-8 hours.
Remove chicken and shred or cut into bite sized pieces. Stir back into soup.
Before serving, stir in lime juice, taste and re-season with salt, more curry paste, red pepper flakes, if necessary.
Serve over brown rice or noodles and garnish with cilantro and peanuts.