In a medium bowl, whisk together the creamy peanut butter, sesame oil, lime juice, minced garlic, minced ginger, low-sodium soy sauce, honey, water, and red pepper flakes. Adjust the consistency with more water if needed; you want a smooth, pourable sauce.
In a large skillet or wok, heat the extra-virgin olive oil over medium-high heat. Once hot, add the bite-sized chicken pieces. Cook for about 5-7 minutes, stirring occasionally, until the chicken is golden brown and cooked through. Make sure to season lightly with salt and pepper.
Toss in the chopped broccoli and sliced red bell peppers. Sauté for another 3-4 minutes until the vegetables are tender but still vibrant and crisp.
Pour the peanut butter sauce over the chicken and vegetables, stirring well to coat everything evenly. Let it simmer for a few minutes, allowing the sauce to thicken slightly and the flavors to meld together.
Remove from heat and serve the Peanut Butter Chicken over a bed of cooked brown rice. Garnish with chopped green onions, fresh cilantro, and chopped peanuts for added crunch and flavor.