Heat oven to 425°F (220°C). High heat equals crisp edges.
Line a large rimmed sheet pan with parchment for easy cleanup.
Pat chicken dry with paper towels.
In a small bowl, mix 1 tablespoon olive oil, 1/2 teaspoon salt, 1/2 teaspoon pepper, garlic powder, onion powder, smoked paprika, and thyme.
Rub the seasoning all over the chicken, lifting the skin gently to season underneath for more flavor.
Toss potatoes with 1–2 tablespoons olive oil, 1/2–3/4 teaspoon salt, and a pinch of pepper.
Scatter them cut side down on the sheet pan. Roast for 15 minutes to jump-start crisping.
Pull the pan out, push potatoes to the sides, and nestle chicken in the center, skin side up.
Return to oven and roast for 15 minutes.
Toss green beans with 1 tablespoon olive oil, 1/2 teaspoon salt, and pepper. Add red pepper flakes if you like heat.
Spread beans in open spaces around the chicken and potatoes.
Roast another 12–15 minutes, until beans are tender-crisp, potatoes are golden, and chicken hits an internal temp of 165°F.
Grate lemon zest over everything and squeeze a little fresh lemon juice to brighten the flavors.
Optional: Sprinkle with Parmesan and chopped parsley.
Rest chicken for 5 minutes so juices settle, then serve hot.
