Pat 6 chicken thighs dry with paper towels and season all over with ¾ teaspoon kosher salt.

Heat 1 tablespoon olive oil in a large 12-inch skillet over medium heat until shimmering. Add the chicken skin-side down and sear until golden-brown, 13 to 15 minutes. Flip and cook until the second side is golden-brown, 10 to 12 minutes more.

Turn off the heat. Transfer the chicken to a large plate skin-side up (it will not be cooked through). Remove all but 1 tablespoon of fat in the pan.

Add 1 finely chopped medium shallot and 3 minced garlic cloves to the pan. Cook over medium heat until translucent, about 1 minute. Add ½ cup dry white wine and simmer, scraping up any browned bits stuck to the bottom of the pan, about 30 seconds. Add ¾ cup heavy cream, ½ cup low-sodium chicken broth, and 1 tablespoon coarsely crushed whole peppercorns. Bring to a rapid simmer, stirring regularly.

Reduce the heat to medium-low. Return the chicken skin-side up to the pan and pour in any accumulated juices from the plate. Simmer until the sauce is thick enough to coat the back of a spoon and the chicken is cooked through, 8 to 10 minutes. Transfer the chicken to a serving platter.

Stir 1 tablespoon finely grated lemon zest and 2 tablespoons of the finely grated Pecorino Romano cheese into the sauce. Spoon the sauce around the chicken. Garnish with the remaining 1 tablespoon finely grated Pecorino Romano cheese and chopped fresh parsley leaves if desired. Serve with lemon wedges and more grated Pecorino Romano cheese if desired.