Preheat oven to 300°.
To prepare meringues, cover a large baking sheet with parchment paper. Draw 4 (3 1/2-inch) circles on paper. Turn paper over, and lay flat on pan.
Place egg whites in a medium bowl; beat with a mixer at high speed until foamy. Gradually add 1/3 cup sugar, 1 tablespoon at a time, beating until stiff peaks form. Divide egg white mixture evenly among the 4 drawn circles. Shape meringues into nests with 1-inch sides using the back of a spoon.
Bake at 300° for 1 hour or until meringues are lightly browned and dry. Remove from oven, and let cool completely (about 30 minutes) on pan. Carefully remove meringues from paper.
While meringues cool, drain cherries, reserving all liquid. Combine reserved cherry juice, 2 tablespoons sugar, crème de cassis, and next 4 ingredients in a small saucepan, stirring well with a whisk. Stir in cherries. Cook over medium heat 7 minutes or until mixture is thick and bubbly, stirring constantly. Remove from heat, and let cool completely.
Place meringues on dessert plates. Spoon cherry mixture evenly into meringue shells; sprinkle with shaved white chocolate.