Grill one piece to eat immediately, hot. And the second - for tomorrow, cold, in sandwiches.
For the barbecue sauce, combine all ingredients in a saucepan, bring to a boil, stirring constantly, and cook over low heat for 2-3 minutes. Cool completely.
Peel the garlic and cut lengthwise into strips. Stuff the meat with garlic. The most convenient way to do this is to stick a thin sharp knife with a narrow blade into the meat to a depth of 5-7 cm. Without removing the blade, turn it in the pulp by 90 ° - you will have a hole where you need to put a couple of garlic sticks, then carefully remove knife.
Lubricate the neck with a couple of spoons of barbecue sauce on all sides, as if rubbing it into the meat, cover with a film and leave to marinate for 2 hours at room temperature.
Kindle the coals - they should burn out and be covered with gray ash. Quickly fry the meat until golden brown, wrap in 3 layers of foil. Rake the coals to the edges of the boiler, put the neck in the center. Roast, turning every 10 minutes, until the internal temperature of the meat reaches 62°C (determine with an electronic thermometer). Remove the foil, brush the meat with the sauce, fry on all sides, 10 minutes. Put on a dish and cover with foil. Leave to "rest" for 20 minutes. Then slice and serve with sauce.