In a 5 - 7 quart slow cooker, mix together coconut milk, chicken broth, red curry paste, brown sugar, coriander, cumin, ginger, and garlic. Sprinkle a pinch of salt (about 1/4 teaspoon).
Add chicken, carrots, and onions to the slow cooker, and immerse lemongrass in the broth. Cover and cook on low heat until the chicken is thoroughly cooked and tender, approximately 5 hours. Add bell pepper during the last 45 minutes of cooking.
Take out the chicken from the slow cooker and let it rest for a few minutes, then shred it. Remove the lemongrass if you use it.
Stir peanut butter, lime juice, and fish sauce into the mixture in the slow cooker. Toss in the shredded chicken and half of the cilantro.
Season with a bit more salt to taste (I added another 1/4 teaspoon). Serve the delicious dish warm with rice, sprinkle peanuts on top, and garnish with the remaining cilantro.