Pat 2 pounds boneless, skinless chicken thighs dry with paper towels. Season all over with 1/2 teaspoon of the kosher salt.

Heat 1 tablespoon olive oil in a 12-inch cast iron or stainless steel skillet over medium-high heat until shimmering. Add the chicken in a single layer and sear until browned, 6 to 8 minutes per side. Transfer the chicken to a plate (it will not be cooked through).

Reduce the heat to medium. Add 2 tablespoons unsalted butter to the skillet. When melted, stir in 1 finely chopped medium shallot and 2 minced garlic cloves. Cook until translucent, about 1 minute. Remove the pan from the heat. Add 1/4 cup Cognac. Return the pan to medium heat and simmer, scraping up any browned bits stuck to the bottom of the pan, until almost evaporated, about 1 minute.

Add 3/4 cup heavy cream, 1/2 cup low-sodium chicken broth, 1 tablespoon coarsely crushed whole peppercorns, 1 teaspoon Dijon mustard, 3 fresh thyme sprigs, and the remaining 1/2 teaspoon kosher salt. Bring to a rapid simmer, stirring regularly.

Return the chicken to the pan in a single layer and pour in any accumulated juices on the plate. Cook until the sauce is thick enough to coat the back of a spoon and the chicken is cooked through, 6 to 8 minutes.

Remove and discard the thyme stems. Stir in 1 tablespoon finely chopped fresh parsley. Garnish with more chopped parsley and serve with lemon wedges if desired.