Slice chicken breast into thin, bite-sized strips.
Wash and chop Chinese broccoli into 2-inch pieces, separating the thick stems from the leafy tops.
Heat avocado oil in a large wok or skillet over medium-high heat until shimmering.
Add chicken to the wok and sear until golden brown and cooked through, about 5-6 minutes.
Remove chicken from the pan and set aside.
Add the thick broccoli stems to the wok with a splash of water, covering for 2 minutes to steam-soften.
Uncover and add the broccoli leaves, minced garlic, and ginger, sautéing until the leaves are wilted and fragrant.
Return the chicken to the pan and stir in the tamari, toasted sesame oil, and red pepper flakes.
Toss everything together for 1 minute to glaze the ingredients evenly.
Serve the stir-fry over the warm brown rice and garnish with sesame seeds.