The first thing to do, which you'll want to do a bit in advance is to whisk together all the marinade ingredients in a small bowl or a measuring cup. Set aside about half of it to season the veggies with. Then place the chicken either in a large, shallow bowl or a gallon sized Ziploc bag and pour the rest of the marinade over the top of it. Coat the chicken really well, then cover the bowl and set it in the fridge to marinate for at least 30 or so minutes.
Preheat the oven to 425F. Line a large baking tray or roasting pan with foil and grease it. Set it aside.
While the chicken marinates, you can begin prepping your veggies. I just chop the potatoes in half if they're small, in quarters if they're on the bigger side. Then peel and chop the carrots into larger, diagonal pieces. Leave the garlic as whole, unpeeled cloves. Toss all of the veggies, except for the garlic, with the set aside marinade.
Take the chicken out of the marinade and set it onto the prepared baking tray. Arrange all of the veggies around and between the chicken. Just place the garlic in different spots nestled into the veggies.
Bake for about 35-45 or so minutes, or until the veggies are fork tender and the chicken is at an internal temperature of 165F. Remove it from the oven and grate some parmesan cheese over the top of it all (optional but delicious).
Serve immediately and enjoy! Refrigerate any leftovers.