Whisk the peanut butter, sesame oil, lime juice, 2 cloves of garlic, 1 tablespoon of ginger, 1 tablespoon of soy sauce, honey, water, and red pepper flakes until smooth.
Heat 1 tablespoon of olive oil in a large skillet, cook the chicken for 5 to 6 minutes until browned and cooked through, then transfer it to a plate.
Add the remaining olive oil, broccoli, and red bell peppers to the skillet and cook for 6 to 8 minutes until crisp-tender.
Stir in the remaining garlic, ginger, and soy sauce with half of the green onions, then cook for 1 minute.
Return the chicken to the skillet, pour in the peanut sauce, and simmer until the sauce thickens and coats the chicken and vegetables.
Sprinkle with the remaining green onions and serve hot, with rice, cilantro, or chopped peanuts if desired.