Heat the oven to 425°F and set a rimmed sheet pan inside while it heats.
Toss the broccoli with 2 tablespoons olive oil, half the salt and half the black pepper, then spread it cut-side down on the hot pan and roast for 8 minutes.
Rub the chicken with the remaining olive oil, salt, black pepper and garlic powder, then place the cutlets between the broccoli pieces.
Roast for 12 to 15 minutes, until the broccoli is browned and the thickest chicken cutlet reaches 165°F.
Stir the lemon zest and juice into the melted butter, spoon it over the chicken and broccoli and serve from the pan.