Place the chicken breasts in the bottom of the slow cooker. Add the broccoli florets, sliced red bell pepper, and shredded carrots on top.
In a mixing bowl, whisk together the peanut butter, soy sauce, lime juice, minced garlic, grated ginger, chicken broth, honey, and red pepper flakes until smooth.
Pour the peanut sauce over the chicken and vegetables in the slow cooker. Cover and cook on low for 6 hours or high for 3 hours.
Remove the chicken, shred it with two forks, then return it to the slow cooker and stir everything together to coat evenly.
Serve over cooked brown rice. Top each portion with chopped roasted peanuts and fresh cilantro.