Preheat the oven to 400°F (200°C).
Place the potato wedges in a large saucepan, cover with cold water, add a pinch of salt, bring to a boil over medium-high heat and cook until just tender, about 8 minutes; drain and set aside.
On a cutting board, pile the reserved rosemary leaves, smashed garlic, 2 teaspoons salt, and red pepper flakes; finely mince and mash into a paste with a large knife, then transfer to a bowl.
Stir the juice of 1 lemon and 2 tablespoons olive oil into the rosemary-garlic paste, add the chicken, and turn to coat each piece thoroughly.
Heat a large cast-iron or ovenproof skillet over medium-high heat. Add the chicken and sear, covered, until browned on the bottom, about 5 minutes; flip and brown the other side for 2–3 minutes.
Brush the bottom of a large baking dish with the reserved 1 tablespoon olive oil. Arrange the seared chicken in the center, place the parboiled potato wedges around the chicken, and add the mushrooms to the dish.
Tuck the remaining rosemary sprigs and the squeezed lemon halves into the baking dish. Drizzle the juice of the remaining lemon and any leftover garlic-lemon mixture over the chicken and potatoes.
Roast uncovered in the preheated oven until the chicken is cooked through and potatoes are golden, about 1 hour; check that chicken reaches a safe internal temperature and adjust time as needed.
Remove from the oven and let rest a few minutes before serving.
