Line 8 muffin cups with paper liners. Melt the white chocolate in top of double boiler over simmering water, stirring until smooth. Spoon 1 tablespoon melted chocolate into each paper liner. Using a pastry brush, coat the chocolate evenly over the bottom and up the sides of the liners. Freeze until the chocolate is firm, about 30 minutes. Remelt the white chocolate in the bowl. Spoon 1 tablespoon into each cup and brush over the bottom and up the sides, forming a second coat. Freeze until completely set, about 1 hour.
Melt the bittersweet chocolate in top of a clean double boiler over simmering water, stirring until smooth. At this point, set aside to cool completely.
Using an electric mixer, beat the cream and sugar in a large bowl until soft peaks form. Set the whipped cream aside.
Using an electric mixer, beat the mascarpone cheese, melted bittersweet chocolate, orange peel, and vanilla in a large bowl just until smooth and glossy, about 30 seconds (do not overmix). Fold the whipped cream into the chocolate mixture in 2 batches. Transfer the mousse to a pastry bag fitted with a star tip. Pipe the mousse into the white chocolate cups. Sprinkle the white chocolate curls over the mousse and serve immediately, or cover and refrigerate overnight, and then let stand at room temperature 1 hour before serving.