Preheat your oven to 425°F (220°C) and line a large rimmed baking sheet with parchment paper.
Peel and dice the sweet potato into 1/2-inch cubes, then toss them directly on the baking sheet with half of the olive oil, half of the sea salt, and half of the black pepper.
Spread the potatoes in a single layer and roast for 10 minutes to give them a head start.
While potatoes roast, pat the chicken breast dry with a paper towel and rub it with the remaining olive oil, minced garlic, dried oregano, and a squeeze of juice from the lemon half.
Remove the baking sheet from the oven, move the potatoes to one side, and place the chicken and broccoli florets on the other side.
Season the broccoli with the remaining salt and pepper, and place the remaining lemon slices over the chicken and vegetables.
Return the pan to the oven and bake for 18 to 22 minutes, or until the chicken reaches an internal temperature of 165°F and the broccoli is slightly charred.
Allow the chicken to rest for 5 minutes before slicing and serving alongside the roasted vegetables.