In a large skillet or wok, heat the vegetable oil over medium-high heat. Add the chicken pieces and cook until browned and cooked through, about 5-7 minutes. Remove the chicken from the skillet and set aside.
In the same skillet, add the red bell pepper, broccoli, and carrot. Stir-fry for about 4-5 minutes until the vegetables are tender-crisp.
Add the minced garlic and ginger to the skillet and cook for an additional 1 minute until fragrant.
In a small bowl, whisk together the peanut butter, soy sauce, honey, rice vinegar, sesame oil, and red pepper flakes (if using) until smooth.
Return the cooked chicken to the skillet and pour the peanut sauce over the chicken and vegetables. Stir well to coat everything evenly and heat through for about 2-3 minutes.
Serve the stir-fry over cooked rice or noodles. Garnish with chopped green onions and crushed peanuts.