Preheat your oven to 400°F and line a large rimmed baking sheet with parchment paper for easy cleanup.
Cut the chicken breast into uniform 1-inch bite-sized pieces and place them into a large mixing bowl.
Add the fresh broccoli florets to the bowl with the chicken pieces.
In a small glass jar or bowl, whisk together the olive oil, toasted sesame oil, tamari, garlic powder, ground ginger, sea salt, and black pepper until well combined.
Pour the savory marinade over the chicken and broccoli, tossing thoroughly with tongs to ensure every piece is evenly coated.
Spread the mixture in a single layer across the prepared baking sheet, making sure the pieces are not crowded so they roast rather than steam.
Bake for 18 to 20 minutes until the chicken is cooked through and the broccoli edges are slightly charred and tender.