4 lamb rib chops (3 to 5 ounces each) fat trimmed from bones
1 tablespoon butter
8 ounces mixed mushrooms (shiitake stems discarded), all others trimmed, caps and stems coarsely chopped
Make mint sauce: In a small bowl, combine vinegar, mustard, and honey. Whisk in oil and mint. Season with salt and pepper; set aside. If making ahead: Cover and refrigerate up to 1 day. Before serving, bring to room temperature, and whisk.
Heat a large skillet over medium-high. Season lamb with pepper. Sprinkle 1 teaspoon coarse salt evenly in skillet. Add chops; cook 2 to 4 minutes per side for medium-rare. Transfer to a plate; cover loosely with aluminum foil to keep warm.
Melt half the butter in a medium skillet over medium heat. Add mushrooms; season with salt and pepper. Cook until browned and softened, 4 to 5 minutes. Add 2 tablespoons water; stir, scraping up browned bits, and cook until liquid has evaporated, about 1 minute. Remove from heat. Stir in remaining butter; season with salt and pepper. Arrange chops on serving plates, and top with mint sauce. Serve with mushrooms.