Preheat your oven to 400°F and line a large baking sheet with parchment paper for easy cleanup.
Peel and dice the sweet potato into 1-inch cubes, then toss them on one side of the baking sheet with 0.5 tablespoons of olive oil and a pinch of the sea salt.
In a small bowl, whisk together the remaining olive oil, lemon juice, lemon zest, oregano, garlic powder, remaining sea salt, and black pepper to create a marinade.
Place the chicken breast on the other side of the baking sheet and brush the lemon-herb mixture evenly over all sides of the meat.
Bake for 20 to 25 minutes, or until the chicken reaches an internal temperature of 165°F and the sweet potatoes are fork-tender and slightly browned.
While the chicken rests for a few minutes, steam the broccoli florets in a steamer basket over boiling water for 5 minutes until they are bright green and tender-crisp.
Slice the chicken against the grain and serve it alongside the roasted sweet potatoes and steamed broccoli, drizzling any extra pan juices over the chicken.