Preheat the oven to 425°F (220°C). This is a hot roast that helps the skin get crisp and the potatoesStation to brown nicely.
Pat the chicken dry. A dry surface soaks up the seasonings better and yields crisper skin. Rub the chicken with 1 teaspoon of salt, pepper, oregano, and thyme.
In a large bowl, toss the potato halves with 1 tablespoon olive oil, a pinch of salt, and half the minced garlic. Spread them in a single layer on a large baking sheet or a shallow roasting pan.
Nestle the seasoned chicken thighs among the potatoes. Drizzle the remaining oil over the chicken, then sprinkle with lemon zest, lemon juice, and the remaining garlic. If you like extra brightness, add a few lemon slices to the pan.
Pour the broth or water into the pan—this helps keep the potatoes moist and creates a little burst of steam as the dish roasts.
Roast for 25 minutes, then give the pan a quick stir to keep everything from sticking and to promote even browning. Continue roasting for another 15-20 minutes, until the chicken reaches an internal temperature of 165°F (74°C) and the potatoes are tender and golden.
If you want extra crispiness on the skin, switch to broil for 2-3 minutes at the end, watching carefully so nothing burns.
Remove from the oven and let rest for 5 minutes. Taste and adjust salt if needed. Scatter with parsley if you’re using it and serve straight from the pan.