Preheat the oven to 425°F (220°C).
In a large bowl, toss the halved baby potatoes with 1 tablespoon of olive oil, 1/2 teaspoon salt, 1/4 teaspoon black pepper, 1/2 teaspoon garlic powder, and 1/2 teaspoon dried rosemary until evenly coated.
Spread the potatoes in a single layer on a large sheet pan and roast in the preheated oven for 15 minutes.
While the potatoes roast, pat the chicken thighs dry with paper towels.
In a small bowl, combine the remaining 2 tablespoons of olive oil, 1/2 teaspoon salt, 1/4 teaspoon black pepper, 1/2 teaspoon garlic powder, 1/2 teaspoon dried thyme, 1 teaspoon paprika, and minced garlic to create a marinade.
Brush the chicken thighs evenly with the marinade mixture.
After the potatoes have roasted for 15 minutes, remove the sheet pan from the oven and add the chicken thighs skin-side up, spacing them evenly among the potatoes.
Add the broccoli florets to the sheet pan and drizzle with fresh lemon juice and a light drizzle of olive oil if desired. Toss broccoli lightly to coat.
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), the potatoes are tender, and the broccoli is crisp-tender.
If desired, broil for 2-3 minutes at the end to crisp the chicken skin.
Remove from oven and let rest for 5 minutes before serving.