Heat the oven. Set it to 425°F (220°C). Place a large sheet pan on the middle rack while it heats. A preheated pan helps the chicken and broccoli sear right away.
Mix the lemon-garlic sauce. In a small bowl, whisk the lemon zest, lemon juice, minced garlic, honey, Dijon, 2 tablespoons olive oil, red pepper flakes (if using), oregano, paprika, 1 teaspoon salt, and several grinds of black pepper.
Taste and adjust for salt and acidity.
Prep the chicken. Pat the chicken dry with paper towels. In a medium bowl, toss it with half the lemon-garlic sauce until coated. Let it sit while you prep the broccoli, 5–10 minutes.
Prep the broccoli. In another bowl, toss the broccoli with the remaining 1 tablespoon olive oil and a generous pinch of salt and pepper.
Keep the rest of the sauce for finishing.
Arrange on the hot pan. Carefully remove the pan from the oven. Spread the chicken pieces on one side in a single layer, leaving space between pieces. Add the broccoli to the other side.
This spacing helps everything brown instead of steam.
Roast. Cook for 10 minutes. Stir the broccoli, flip the chicken pieces, and roast another 8–12 minutes, until the chicken is cooked through (internal temp 165°F/74°C) and the broccoli edges are caramelized.
Finish with sauce. Drizzle the reserved lemon-garlic sauce over the hot chicken and broccoli. Toss right on the pan so the heat softens the garlic and glazes everything.
Adjust salt and pepper to taste.
Garnish and serve. Scatter chopped parsley over the top and add lemon wedges on the side. Serve as is, or spoon over rice, couscous, or orzo to catch the extra juices.