Place a grill wok or grill basket on the rack of an uncovered grill directly over medium coals and heat for 5 minutes. Meanwhile, toss apricots with 2 tablespoons of the mint syrup. Brush pineapple rings with 2 tablespoons of the mint syrup. Sprinkle apricots and pineapple with nutmeg.
Place apricots in the preheated grill wok or basket. Place pineapple directly on the grill rack. Grill for 5 to 8 minutes or until heated through, turning gently halfway through cooking time. (For gas grill, preheat grill. Reduce heat to medium. Place grill wok or grill basket on grill rack over heat for 5 minutes. Cover and grill as above.) Remove fruit from grill; cool slightly.
To serve, quarter the pineapple slices. In a large serving bowl toss together the apricots, pineapple, and remaining Mint Syrup in a large glass serving bowl. Sprinkle with additional freshly grated nutmeg and garnish with fresh mint. (Fruit mixture can be held at room temperature up to 2 hours.) Makes 12 servings.
In a medium saucepan combine water, sugar, mint, and lemon peel. Gently crush the mint with the bowl of a ladle or a wooden spoon. Bring to boiling, stirring to dissolve sugar. Reduce heat and simmer, uncovered, for 10 minutes, stirring occasionally. Remove from heat and let mixture cool for 1 hour. Strain, discarding mint and lemon peel. Transfer to a glass jar, cover, and refrigerate up to 1 week. Makes 1 to 1-1/4 cups syrup.