Preheat your oven to 400°F and line a large baking sheet with parchment paper for easy cleanup.
Peel the sweet potato and cut into 1/2-inch cubes, then trim and halve the Brussels sprouts.
Toss the sweet potatoes and sprouts on the baking sheet with 0.5 tbsp olive oil, 0.25 tsp salt, and 0.25 tsp smoked paprika.
Roast the vegetables for 20-25 minutes, tossing halfway through, until the potatoes are tender and the sprouts are golden and crispy.
While the vegetables roast, season the chicken breast evenly on both sides with the remaining salt, pepper, garlic powder, and smoked paprika.
Heat the remaining 0.5 tbsp olive oil in a cast-iron or heavy skillet over medium-high heat.
Place the chicken in the hot skillet and sear for 6-7 minutes per side until the internal temperature reaches 165°F and the outside is beautifully browned.
Transfer the chicken to a plate and let it rest for 5 minutes to lock in the juices before slicing.
Serve the sliced chicken alongside the roasted vegetables and garnish with finely chopped fresh rosemary.