Season pork chops generously with salt and pepper. Heat oil in a large skillet over medium-high heat and cook pork chops until browned, 2 to 3 minutes per side. Remove from skillet and place on a plate. Cover with aluminum foil to keep warm.

Melt butter in the same skillet and reduce heat. Add shallot and cook until soft and translucent, about 5 minutes. Add thyme and rosemary. Cook and stir for 1 minute. Add kale in batches and cook until wilted, about 5 minutes more.

Stir together mustard, honey, sherry, and cider in a cup. Place pork chops on top of kale in the skillet and pour mustard sauce on top. Bring to a boil and reduce heat. Cover and cook over low heat until pork is cooked through, about 10 minutes more.