Preheat your oven to 425°F (220°C) and line a large sheet pan with parchment paper.
In a small bowl, mix the olive oil, lemon zest, lemon juice, garlic, rosemary, thyme, paprika, salt, and pepper.
Add the potatoes and carrots to the pan and toss them with a third of the herb mixture. Roast for 10 minutes to give them a head start.
Toss the chicken with half of the remaining mixture. Toss the broccoli with the rest.
Take the pan out of the oven. Push the potatoes and carrots to the sides, then add the chicken in the center and the broccoli around it.
Roast for 25 minutes, until the chicken reaches 165°F (74°C) and the vegetables are golden at the edges.
Rest the chicken for 5 minutes, then sprinkle with fresh parsley and a squeeze of lemon. Serve hot.