Preheat the oven to 425°F (218°C) and line a large sheet pan with parchment paper.
Whisk together olive oil, lemon juice, lemon zest, honey, minced garlic, Italian seasoning, sea salt, and black pepper to make the marinade.
In a bowl, toss the potatoes with 3 tablespoons of the marinade and 2 tablespoons grated Parmesan until evenly coated; spread them in a single layer on one side of the prepared sheet pan.
Bake the potatoes for about 20 minutes, until they begin to brown.
While the potatoes bake, toss the chicken thighs with 1/2 cup of the marinade in a bowl and let sit (up to 24 hours refrigerated if preparing ahead).
Also toss the broccoli with the remaining marinade in the same bowl used for the potatoes.
When the potatoes are starting to brown, remove the pan and push the potatoes to one third of the pan; add the broccoli and chicken to the remaining space, allowing excess oil to drip from the chicken before placing it on the pan.
Return the sheet pan to the oven and bake for about 25 minutes more, or until the chicken reaches an internal temperature of 165°F (74°C); check at 20 minutes and then every 2–3 minutes as needed.
Remove the pan and let the chicken rest about 5 minutes before serving; for extra-crispy potatoes, broil on high for 2–3 minutes after removing the chicken.
Serve with additional grated Parmesan, extra lemon zest, and chopped parsley if desired.
