Preheat oven to 425°F.
Whisk together marinade ingredients. Add 3 tablespoons of the marinade to the potatoes along with the parmesan and toss to fully and evenly coat. Line a large sheet pan with parchment paper and evenly arrange the potatoes in a single layer.
Bake the potatoes in preheated oven for about 20 minutes or until they start to brown.
While potatoes cook, toss 1/2 cup of the marinade with the chicken thighs and allow them to marinate. (You can do this step up to 24 hours in advance if desired.) Toss remaining marinade with the broccoli (save a dish and use the same bowl you used for the potatoes!)
When the potatoes start to brown, remove sheet pan from oven and shift them to one third of the pan. Add the broccoli and chicken, allowing excess oil to drip from the chicken before adding to pan.
Bake for about 25 minutes or until the chicken has reached an internal temperature of 165°F. For best results, check the temperature at 20 minutes and then every 2-3 minutes.
Remove the pan from the oven and allow to rest for about 5 minutes before serving. For extra crispy potatoes, you can also broil on high for about 2-3 minutes after removing the chicken.
Serve with freshly grated parmesan, extra lemon zest and some chopped parsley. Enjoy!