Preheat the oven to 425°F. Place a large rimmed sheet pan in the oven while it heats so the pan gets hot.
Cut the potatoes into evenly sized chunks about 1½ inches wide. Place them in a bowl and toss with 2 tablespoons olive oil, ¾ teaspoon kosher salt, ½ teaspoon black pepper, and ½ teaspoon paprika until well coated.
Carefully remove the hot sheet pan from the oven and spread the potatoes out in a single layer. Roast for 15 minutes while you prepare the chicken.
Pat the chicken thighs very dry with paper towels. This step matters because dry skin is what makes the chicken crisp.
In a small bowl, mix the remaining 2 tablespoons olive oil, minced garlic, zest from the lemon, remaining ¾ teaspoon kosher salt, remaining ¼ teaspoon black pepper, oregano, onion powder, crushed red pepper flakes, and remaining ½ teaspoon paprika.
Rub the garlic lemon mixture all over the chicken thighs, including under the skin if you can loosen it slightly.
After the potatoes have roasted for 15 minutes, remove the pan and push the potatoes slightly apart to make space. Place the chicken thighs skin-side up between the potatoes.
Return the pan to the oven and roast for 35 to 40 minutes, until the chicken skin is deeply golden and crisp and the internal temperature reaches 175°F to 180°F in the thickest part of the thigh.
Cut the lemon in half and squeeze the juice over the chicken and potatoes immediately after removing from the oven. Sprinkle with chopped parsley if using.
Let rest for 5 minutes before serving so the juices settle and the potatoes finish crisping slightly.