Preheat your oven to 400°F (200°C) and line a large baking sheet with parchment paper for easy cleanup.
Peel the sweet potato and cut it into 1-inch cubes, then slice the mushrooms into thick halves.
In a medium bowl, toss the sweet potato cubes and mushrooms with half of the olive oil, the smoked paprika, and a pinch of the sea salt and black pepper.
Place the chicken breast on one side of the baking sheet and rub with the remaining olive oil, dried thyme, garlic powder, and the rest of the salt and pepper.
Spread the seasoned vegetables in a single layer on the other side of the baking sheet around the chicken.
Roast in the oven for 20 to 25 minutes, or until the chicken reaches an internal temperature of 165°F and the sweet potatoes are fork-tender.
Remove from the oven and let the chicken rest for 5 minutes before slicing it into strips.
Plate the roasted chicken and vegetables, serving with a dollop of cool Greek yogurt on the side to balance the smoky heat.