Preheat oven to 425°F. Line a large sheet pan with parchment paper or foil.
Toss potatoes with 1½ tablespoons olive oil, ½ teaspoon salt, ¼ teaspoon pepper, ½ tablespoon Italian seasoning, and ½ teaspoon onion powder. Spread on pan in a single layer.
Roast potatoes for 15 minutes.
While potatoes roast, pat chicken dry. Toss chicken with remaining olive oil, melted butter (if using), garlic, remaining Italian seasoning, oregano, remaining onion powder, remaining salt and pepper, red pepper flakes (if using), and lemon zest.
Remove pan from oven. Push potatoes to one side and add chicken in a single layer. Roast 15 minutes.
Toss green beans with a tiny drizzle of olive oil (about 1 teaspoon) and a pinch of salt and pepper. Add to pan.
Roast 10 to 12 minutes more, until chicken reaches 165°F and potatoes are fork-tender.
Sprinkle Parmesan over the hot pan. Rest 2 to 3 minutes so it melts. Finish with lemon juice and parsley before serving.