No need to peel the apricots for this fragrant sorbet—the skin adds lovely flecks of color to the final product.
1. Stir together honey and 1 cup water in saucepan. Bring to a boil, stirring to dissolve honey. Remove from heat, and add rosemary sprigs. Cover, and cool.
2. Purée apricot halves in food processor until very smooth. (You should have 2 1/2 cups.) Transfer to bowl, and stir in honey mixture and lemon juice. Remove rosemary sprigs, and discard.
3. Chill in refrigerator until cold, then churn in ice cream maker according to manufacturer’s directions. Transfer to 1-quart container, and freeze.