Slice the chicken into thin, even strips and place it in a bowl with black pepper, half of the garlic, and half of the ginger, mixing gently to coat.
Heat a large skillet over medium-high heat, add the oil, and place the chicken in a single layer once hot.
Cook the chicken undisturbed for 2–3 minutes until lightly golden, then flip and cook just until done before removing it from the pan.
Add the remaining garlic and ginger to the same skillet and cook briefly until fragrant.
Add the broccoli and bell peppers and stir-fry until crisp-tender and vibrant.
Return the chicken to the skillet, pour in the soy sauce or coconut aminos, and toss gently until everything is evenly coated and heated through.
Remove from heat and serve immediately or portion for meal prep.