Slice the chicken breast into thin, bite-sized strips and season evenly with the sea salt and black pepper.
In a small glass jar or bowl, whisk together the coconut aminos, toasted sesame oil, minced garlic, grated fresh ginger, and arrowroot powder until smooth.
Heat the avocado oil in a large stainless steel skillet or wok over medium-high heat until it begins to shimmer.
Add the chicken strips to the hot pan in a single layer and sear for 3 minutes per side until golden brown and fully cooked through, then transfer to a plate.
Add the broccoli florets and sliced red bell pepper to the same skillet with two tablespoons of water; cover with a lid for 2 minutes to steam the vegetables until tender-crisp.
Remove the lid, return the chicken and any juices to the pan, and pour the garlic sauce over the mixture.
Toss everything constantly for 1 minute as the sauce bubbles and thickens into a glossy glaze that coats the chicken and vegetables.