Preheat the oven to 425°F. Line a large rimmed sheet pan with parchment paper or lightly grease it.
Add the potatoes to the sheet pan. Toss with 1 tablespoon olive oil, ½ teaspoon salt, ¼ teaspoon garlic powder, and black pepper. Spread into a single layer and roast for 15 minutes.
While the potatoes roast, stir together the honey, tamari (or soy sauce), garlic, rice vinegar, and ground ginger in a small bowl.
Remove the sheet pan from the oven. Add the chicken and season with the remaining ¼ teaspoon salt and ¼ teaspoon garlic powder. Pour half of the honey garlic sauce over the chicken and toss to coat.
Return the sheet pan to the oven and bake for 8 minutes.
Remove the pan from the oven and add the broccoli. Drizzle with the remaining 1 tablespoon olive oil. Pour the remaining honey garlic sauce over the chicken and vegetables and gently toss to coat.
Bake for another 10–15 minutes, or until the potatoes are fork-tender, the broccoli is roasted, and the chicken reaches an internal temperature of 165°F.
For a sticky, caramelized finish, broil for 1–2 minutes. Watch carefully to prevent the honey from burning. Serve warm.