In a small glass bowl, whisk together the tamari, honey, rice vinegar, grated ginger, and minced garlic to create the teriyaki glaze.
Season the chicken breast evenly on both sides with sea salt and black pepper.
Heat the avocado oil in a medium stainless steel or cast iron skillet over medium-high heat.
Place the chicken in the skillet and sear for 5 to 6 minutes per side, or until the internal temperature reaches 165°F and the exterior is golden brown.
While the chicken cooks, steam the broccoli florets in a steamer basket over boiling water for 3 to 4 minutes until they are bright green and tender-crisp.
Remove the chicken from the skillet and let it rest on a cutting board for 3 minutes.
Lower the skillet heat to medium and pour in the teriyaki sauce, scraping up any browned bits from the bottom of the pan. Simmer for 1 to 2 minutes until the sauce thickens into a glossy glaze.
Slice the chicken into strips and toss them back into the skillet to coat thoroughly with the sauce.
Fold the toasted sesame oil into the warm cooked rice.
Plate the sesame rice alongside the steamed broccoli, top with the glazed chicken, and garnish with sesame seeds.