Preheat the oven to 425°F. Line a large rimmed sheet pan with parchment paper or lightly grease it with cooking spray.
Place the cubed sweet potatoes on the prepared sheet pan. Drizzle with 1 tablespoon olive oil.
Add half of the minced garlic, smoked paprika, garlic powder, onion powder, and about half of the salt and black pepper. Add the crushed red pepper flakes, if using.
Toss the sweet potatoes until evenly coated with the oil and seasonings. Spread them into a single layer.
Bake for 15 minutes. Giving the sweet potatoes a head start helps ensure they are tender by the time the chicken is fully cooked.
While the sweet potatoes are roasting, place the chicken pieces in a large mixing bowl. Add the remaining 2 tablespoons olive oil, remaining minced garlic, dried thyme, and remaining salt and black pepper.
Toss until the chicken is evenly coated with the oil and seasonings.
Carefully remove the sheet pan from the oven. Add the seasoned chicken, trimmed green beans, and red onion wedges to the pan.
Gently toss the ingredients to distribute the seasonings, then arrange everything in an even layer.
Return the sheet pan to the oven and roast for 18 to 20 minutes, or until the sweet potatoes are fork-tender and the chicken reaches an internal temperature of 165°F.
Remove from the oven and sprinkle with chopped fresh parsley. Serve warm.