Preheat your oven to 400°F (200°C) and line a large rimmed baking sheet with parchment paper for easy cleanup.
Peel the sweet potato and dice it into uniform 1/2-inch cubes, then cut the chicken breast into similar bite-sized pieces.
Place the chicken and sweet potatoes on the prepared baking sheet, then drizzle with the extra virgin olive oil.
Sprinkle the garlic powder, smoked paprika, sea salt, and black pepper over the chicken and potatoes, tossing thoroughly to ensure every piece is well-coated.
Spread the mixture into a single layer, ensuring there is space between the pieces so they roast rather than steam.
Roast in the oven for 15 minutes.
Remove the pan from the oven, add the broccoli florets to the sheet, and give everything a quick toss to coat the broccoli in the pan juices.
Return the tray to the oven and roast for an additional 10 to 12 minutes until the chicken is cooked through and the sweet potatoes are fork-tender.