Heat the oven. Preheat oven to 425F. Place a large sheet pan or roasting pan in the oven while it heats (optional but helps browning).
Prep the chicken. Remove giblets if needed. Pat chicken very dry with paper towels. Season the cavity with a pinch of salt and pepper, then stuff with lemon halves and garlic (and herbs if using).
Season the outside. In a small bowl, mix salt, pepper, thyme, and paprika. Rub chicken all over with olive oil (and butter if using), then rub seasoning evenly over the skin.
Toss the potatoes. In a bowl, toss potatoes and onion with a drizzle of olive oil and a pinch of salt and pepper.
Assemble. Carefully remove the hot pan. Spread potatoes/onion out in an even layer. Pour broth into the pan (around the edges). Place chicken on top, breast side up. Add garlic halves to the pan if not inside the chicken.
Roast. Roast 60 to 75 minutes, until the thickest part of the thigh reaches 165F to 175F and juices run clear. If potatoes need more color, remove chicken to rest and return potatoes to the oven for 10 minutes.
Rest and serve. Rest chicken 10 to 15 minutes before carving. Serve with potatoes, pan juices, and roasted garlic squeezed on top.