In a small bowl, whisk together the gochujang, tamari, grated ginger, and minced garlic to create a smooth, pungent sauce.
Slice the chicken breast into bite-sized 1-inch cubes and season lightly with the red pepper flakes for an extra kick.
Heat the 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 until golden brown and cooked through.
Remove the chicken from the pan and set aside, then add the broccoli florets and sliced red bell peppers to the same skillet.
Stir-fry the vegetables for 3 minutes until they are bright and tender-crisp, then return the chicken to the pan.
Pour the gochujang sauce over the chicken and vegetables, tossing constantly for 1 minute until everything is coated in a glossy, spicy glaze.
Remove from heat and stir in the toasted sesame oil for a fragrant finish.
Serve the stir-fry over the warm cooked brown rice and garnish with sesame seeds and sliced green onions.