Heat the oven to 400°F/200°C.
Place potatoes and leeks in a large braiser or oven-safe skillet, toss with olive oil, salt, and pepper, and spread evenly. Arrange the chicken pieces on top of the vegetables.
In a bowl, whisk together all the lemon sauce ingredients until smooth. Spoon the sauce over the chicken, then pour the remaining sauce over the vegetables.
Cover the pan and roast for 35 to 45 minutes, until the potatoes are nearly tender. Increase the oven temperature to 425°F/220°C, uncover, and continue roasting until the chicken is browned and the potatoes are fully tender, 30 to 45 minutes more.
For deeper color, broil for 2 to 3 minutes, watching closely. Spoon the pan sauce over the chicken and finish with fresh parsley before serving.