1. Quarter plums; remove pits. Combine plums, honey, jalapeno, sugar, vinegar, and lime juice in a small nonreactive saucepan. Cook over low heat until plums are very soft and juice is slightly thickened, about 30 minutes. If plums are not juicy, add water a little at a time during cooking to avoid scorching. Remove from heat, strain, and discard solids.

2. Heat grill or cast-iron grill pan. Season lamb well with salt and pepper and wrap bones with foil to prevent burning. Grill lamb fat side down for 5 minutes, brush with plum glaze, and turn over. Repeat glazing every minute or so thereafter. For rare lamb, cook until it reaches an internal temperature of 135 degrees, 10 to 12 minutes; cook longer for medium or well. Let the meat rest for 10 minutes after grilling.

3. Toss Oven Dried Plums with some of the remaining glaze. Carve racks into chops. Serve 2 chops per person with the glazed plums; garnish with sprigs of thyme.