How to Make It
Preheat the oven to 350°. In a pie plate, bake the hazelnuts until lightly browned, about 8 minutes. Let cool, then rub the nuts together in a kitchen towel to remove the skins. Finely chop the nuts.
Reduce the oven temperature to 225°. Line a large rimmed baking sheet with parchment paper. Using a 3-inch cookie cutter as a guide, trace six 3-inch circles on the paper, spacing them equally. In a medium stainless steel bowl, using a handheld mixer, beat the egg whites with the cream of tartar at medium speed until soft peaks form. Gradually add the granulated sugar and beat until the meringue is firm and glossy, about 3 minutes. Stir in the vanilla. Set a fine sieve over the bowl and sift the confectioners' sugar over the meringue while folding it in with a rubber spatula. Fold in the hazelnuts.
Drop a large spoonful of meringue inside each of the circles and spread until the circle is filled, then top with more meringue until the vacherin is about 1 inch tall. Repeat. Bake for about 2 hours, or until the meringues are dry, crisp and barely colored. Let cool completely, then gently lift the meringues off the parchment.
Put the softened ice cream in a large bowl and blend in the candied ginger. Cover and freeze until firm, about 1 hour.
Melt the butter in a medium saucepan. Add the water, cream and honey and bring to a simmer over moderately high heat. Put the chocolate in a medium bowl and pour the hot cream on top. Let stand until the chocolate melts, 1 minute, then stir until smooth. Stir in the rum.
Set a meringue on each plate and top with a scoop of ice cream. Pour the sauce over the ice cream, top with a dollop of whipped cream and serve.