Preheat oven to 425°F (220°C) and line a sheet pan with parchment paper.
Whisk together olive oil, garlic, lemon juice, lemon zest, oregano, paprika, salt, and pepper.
Arrange chicken, potatoes, and broccoli on the sheet pan. Pour marinade over everything and toss vegetables to coat; place chicken skin-side up.
Roast for 25–30 minutes, until chicken reaches 165°F (74°C) internally and potatoes are fork-tender. Add broccoli halfway through if it browns too fast.
Let chicken rest 5 minutes, then top with parsley and lemon slices before serving.