Preheat your oven to 400°F (200°C). Line a large, rimmed baking sheet with parchment paper for easy cleanup.
In a small bowl, whisk together the garlic powder, dried oregano, dried thyme, smoked paprika, kosher salt, and black pepper. Set this seasoning blend aside.
On the prepared baking sheet, combine the potatoes, carrots, and red onion. Drizzle with 1.5 tablespoons of olive oil and sprinkle with HALF of the seasoning blend. Toss everything together directly on the pan until the vegetables are evenly coated. Spread them into a single layer.
Roast the vegetables for 15 minutes. This gives the heartier veggies a head start on cooking.
While the vegetables are roasting, place the chicken pieces and broccoli florets in a large mixing bowl. Drizzle with the remaining 1.5 tablespoons of olive oil and sprinkle with the remaining HALF of the seasoning blend. Toss until the chicken and broccoli are well-coated.
After 15 minutes, carefully remove the sheet pan from the oven. Push the partially cooked vegetables to the sides to make space in the center. Add the seasoned chicken and broccoli to the pan in a single layer, ensuring nothing is too crowded.
Return the pan to the oven and roast for another 18-20 minutes, or until the chicken is cooked through (internal temperature reaches 165°F or 74°C), the potatoes are tender, and the broccoli is crisp-tender with slightly charred edges.
Remove from the oven. If desired, garnish with fresh chopped parsley and a squeeze of fresh lemon juice from the wedges before serving. Serve hot, directly from the pan.