Combine rosemary, garlic, peppercorns, soy sauces, salt and oil in a large bowl.
Add to lamb and turn to coat.
Cover and refrigerate 2-3 hours.
Combine hoisin sauce, soy sauce and honey in a bowl.
Mix and set aside.
Combine mango, bell pepper, onion, mint, soy sauces, honey, lemon juice and plum sauce in a bowl; mix well.
Cover and refrigerate until ready to serve.
Preheat broiler with rack placed 4 to 5 inches from heating element.
Place lamb, meat side up, in a foil-lined baking pan.
Broil lamb, meat side up, for 10 to 12 minutes.
Turn, brush with glaze, and broil for 5 to 7 minutes more.
Turn meat again, brush with glaze, and broil for 3 to 4 minutes more.
Slice rack between ribs.
Serve with rice and salsa and garnish with mint leaves.
