Generously load up and light up a charcoal barbecue. The barbecue has to be hot, there are no flames, medium hot coals with light layer of grey ash.
Take the rack out of refrigerator, using a paper towel pat and dry the rack thoroughly, leave at room temperature for 30-40 minutes.
Salt the rack liberally with coarse salt.
With a sharp knife make 6-9 incisions on a rack’s fat side. Stagger the incisions into three rows, fill each incision with part of a rosemary spring.
To avoid burning and crumbling of the rack bones, wrap each bone end with aluminum foil.
Push the hot coals on one half of the barbecue. Put the barbecue grate on, cover and let it heat up for 5 minutes.
Clean the grate with steel brush. Put the rack on the grate, fat side down, close to the coals but not above them, bones away from the coals. You want to roast rack on a passive heat side of the grate. Cook for 4 minutes.
Turn the rack for 180º, still fat side down, but bones towards the coal, cook for another 4 minutes.
Turn the rack to the bone side down, cook for 4 minutes.
Rotate the rack for 180º and cook another 4 minutes.
Insert instant thermometer into middle of the meat and check the temperature. Continue cooking and turning until internal temperature of 55ºC (131ºF) is reached, about 25-30 minutes.
Transfer rack to the plate and let rest for 10 minutes.
Slice rack into 8 sections, sprinkle with freshly cut parsley and serve.