Slice the chicken breast into bite-sized strips and toss in a bowl with arrowroot powder, sea salt, and black pepper until lightly coated.
Heat avocado oil in a large skillet or wok over medium-high heat until shimmering.
Add the chicken to the pan in a single layer and sear for 3-4 minutes per side until golden brown and cooked through.
Remove the chicken from the pan and set aside; add toasted sesame oil to the same pan.
Toss in the broccoli, sliced bell peppers, and snap peas, stir-frying for 3-5 minutes until bright green and slightly tender.
Stir in the minced garlic and grated ginger, cooking for 30 seconds until fragrant.
Return the chicken to the pan and pour in the tamari, tossing everything together for 1 minute to glaze the ingredients.
Garnish with sesame seeds and serve immediately while hot and crispy.