Preheat the oven to 425°F (220°C).
In a large bowl, combine the halved baby red potatoes with 1 tablespoon of olive oil, 1/2 teaspoon salt, 1/4 teaspoon black pepper, and 1/2 teaspoon dried thyme. Toss to coat evenly.
Spread the potatoes in a single layer on a large rimmed sheet pan. Roast in the preheated oven for 15 minutes.
While the potatoes roast, pat the chicken breasts dry with paper towels.
In the same large bowl, combine the chicken breasts with the remaining 1 tablespoon olive oil, garlic powder, smoked paprika, remaining dried thyme, dried rosemary, remaining 1/2 teaspoon salt, remaining 1/4 teaspoon black pepper, and minced garlic. Rub the seasoning evenly over each chicken breast.
After the potatoes have roasted for 15 minutes, remove the sheet pan from the oven. Stir the potatoes and push them to one side of the pan.
Place the seasoned chicken breasts on the other side of the sheet pan, ensuring they are not touching the potatoes.
Return the sheet pan to the oven and roast for an additional 20 minutes, or until the chicken reaches an internal temperature of 165°F (74°C) and the potatoes are tender and golden brown.
Remove the sheet pan from the oven and squeeze fresh lemon wedges over the chicken and potatoes.
Sprinkle chopped fresh parsley over the entire dish before serving.