Preheat oven to 425°F. Season chicken all over with salt and pepper. Arrange chicken skin-side down in a large cold ovenproof skillet.
Cook over medium heat, undisturbed, until skin is crispy and golden brown, about 15–20 minutes. Transfer chicken to a plate.
In the same skillet over medium-high heat, cook onions with 1/4 tsp salt, scraping up browned bits, until softened, about 7 minutes.
Add garlic; cook 1 minute until fragrant. Add wine and simmer until reduced by half, about 3 minutes. Stir in broth and bring to a simmer.
Return chicken skin-side up to the skillet. Transfer to oven and bake uncovered for 30 minutes, until chicken is cooked through.
Transfer chicken to a plate again. With a towel or mitt on the handle, return skillet to stovetop over medium-high heat.
Add cream; bring to a boil. Reduce heat and simmer until slightly thickened, about 3 minutes.
Stir in lemon zest, 1 Tbsp pecorino, and 1 tsp pepper. Season with salt if needed.
Return chicken to skillet with any juices. Top with parsley, remaining pecorino, and extra black pepper. Serve with lemon wedges and more cheese if desired.