In a bowl, whisk together peanut butter, soy sauce, vinegar, honey, ginger, garlic, red pepper flakes, water, and cornstarch until smooth. Set aside.
Heat olive oil in a large skillet over medium-high heat.
Add chicken and cook until browned and cooked through, about 5-6 minutes. Remove from skillet and set aside.
Add broccoli, bell pepper, snow peas, and carrots to the skillet. Stir-fry for 4-5 minutes until just tender.
Return chicken to the skillet and pour in the peanut sauce. Stir well to coat.
Cook for another 2-3 minutes, until the sauce thickens.
Serve over rice and top with green onions and sesame seeds if desired.