In a large wok or pan with high sides, over medium-high heat, add 1 tablespoon of oil.
Add the chicken pieces, salt, pepper, and onion, cooking for 4-5 minutes (or until the chicken is mostly cooked through).
Add the remaining 1 tablespoon oil, broccoli & peppers to the pan and cook for another 5 minutes, over medium-high heat, until chicken is fully cooked.
On a separate burner, cook the pad thai noodles according to the package directions.
In a medium bowl, whisk together the sauce ingredients and set aside.
In the pan, push the cooked vegetables with chicken to the side of the pan and pour in the whisked egg and cook just until scrambled, mixing often. Once the egg is cooked, mix together with the veggies in the pan.
Add the pad thai sauce to the pan, mix, and let it come to a simmer. Mix in the cooked noodles and cook for another 1-2 minutes over medium heat, stirring often, until the sauce has thickened.
Turn off the heat and garnish with chopped scallions, peanuts, bean sprouts, and a drizzle of lime (or place lime wedges onto each bowl).