Heat broiler; set rack 4 inches from heat. In a large skillet, heat butter over medium-high. Add shallots; cook, stirring occasionally, until browned, about 5 minutes. Cover pan; reduce heat to medium. Continue cooking until shallots are soft, about 5 minutes more.
Add apples and wine; cover, and cook until apples are beginning to soften, about 5 minutes. Uncover; cook, stirring, until most of the liquid has evaporated and apples are tender, 2 to 4 minutes more. Remove from heat; cover to keep warm.
While apples are cooking, season pork chops generously with salt and pepper; place on a rimmed baking sheet. Broil until cooked through, 3 to 5 minutes per side. To serve, spoon warm apple mixture over chops.