Trim any excess fat from the chicken breasts and cut into roughly 1-inch pieces.
Whisk together soy sauce, rice vinegar, sesame oil, sweetener, maple syrup, and garlic powder to make the marinade/glaze; reserve 1/4 cup of the mixture for glazing later and set aside.
Place the chicken pieces in a resealable plastic bag or lidded container and pour in the remaining marinade; refrigerate at least 4–5 hours or up to all day.
When ready to cook, preheat the oven to 425°F (220°C). Drain the marinated chicken in a colander.
Line a baking sheet with foil or plan to spray it with nonstick spray. Place the baking sheet in the hot oven to preheat for a minute or two.
If you did not use foil, spray the hot baking sheet with nonstick spray, spread the chicken pieces on the sheet, and bake for 8 minutes.
While the chicken starts cooking, trim and cut broccoli into similar-size florets and toss them in a bowl with 1 tablespoon peanut oil.
After the initial 8 minutes, remove the baking sheet and tuck the oiled broccoli florets among the chicken pieces, return the sheet to the oven, and bake 12–14 more minutes until chicken is cooked through and broccoli is tender to your liking.
Brush the hot chicken and broccoli with the reserved 1/4 cup glaze and sprinkle with black or regular sesame seeds if desired.
Serve hot.