Preheat your oven to 400°F (200°C). Line a large baking sheet with parchment paper for easier cleanup.
In a large bowl, combine the olive oil, minced garlic, lemon zest, lemon juice, oregano, thyme, rosemary, salt, and pepper. Whisk together to create the marinade.
Add the chicken pieces to the bowl and toss to coat evenly. Let it marinate for at least 10 minutes while you prepare the vegetables.
Add the quartered potatoes, red onion wedges, bell pepper pieces, zucchini, and broccoli florets to the same bowl (no need to wash it). Toss the vegetables with any remaining marinade. If the mixture seems a bit dry, you can add another tablespoon of olive oil.
Arrange the marinated chicken and coated vegetables in a single layer on the prepared baking sheet. Ensure there's some space between the pieces for even roasting.
Roast for 25-30 minutes, or until the chicken is cooked through (internal temperature reaches 165°F or 74°C) and the vegetables are tender and slightly caramelized. You can toss them halfway through for more even browning.
Once cooked, remove from the oven. Garnish with fresh parsley if desired.