Preheat the oven to 375°F (190°C). On a large rimmed half-sheet pan, spread potato wedges and onions in a single layer. Drizzle with about 1 tbsp of the oil and season with 1/2 tsp kosher salt and half the black pepper.

Pat chicken dry. Loosen skin and rub the remaining 1/2 tsp kosher salt directly onto the meat. Arrange chicken, skin-side up, among the potatoes and onions.

In a small bowl, combine the minced garlic with the remaining oil; let stand 5 minutes. Whisk in lemon juice, dried thyme, smoked paprika, and remaining black pepper.

Pour the lemon-herb sauce evenly over chicken and potatoes, tucking most garlic under the chicken skin or among the potatoes to prevent scorching. Arrange lemon slices on top. Carefully pour the broth into the side of the pan without washing off the sauce.

Bake uncovered for 45–55 minutes, until the chicken reaches 165°F (74°C) and potatoes are tender when a knife slides in easily.

For crisper skin, move the rack up and broil 2–4 minutes, watching closely; brush any garlic off the tops of the chicken onto the potatoes before broiling.

Scatter olives (if using) and parsley over the top. Rest 5 minutes, then serve warm.