In a bowl, combine the pears with the Moscato d'Asti and let stand at room temperature for 2 to 4 hours.
Preheat the oven to 350°. Butter and flour an 8-by-1-inch round cake pan. Put the hazelnuts on a rimmed baking sheet and bake for 12 minutes, or until richly browned. Transfer the hazelnuts to a kitchen towel and let cool completely. Rub the hazelnuts in the towel to remove the skins. In a food processor, pulse the nuts until they're finely ground; be careful not to overprocess to a paste.
In a large bowl, using a handheld mixer, beat 6 tablespoons of the butter with 1/4 cup of the sugar until light and fluffy. Beat in the egg yolks, 1 at a time, until thoroughly incorporated. Add the vanilla, then fold in the hazelnuts and flour.
In a stainless-steel bowl, beat the egg whites until soft peaks form. Add the remaining 2 tablespoons of sugar and beat until almost-firm shiny peaks form. Stir one-third of the egg whites into the cake batter to lighten it, then fold in the remaining whites. Scrape the batter into the prepared pan and bake for about 20 minutes, or until a cake tester inserted in the center comes out clean. Transfer the cake to a rack and let it cool slightly in the pan. Run a thin knife around the cake and unmold it. Cover loosely with a kitchen towel.
Drain the Moscato d'Asti into a small saucepan. Simmer over low heat until reduced to 3 tablespoons, about 10 minutes. Let the syrup cool, then refrigerate.
In a large skillet, melt the remaining 1 tablespoon of butter. Add the pears and cook over moderately high heat until browned, about 4 minutes per side. Arrange the pear wedges on top of the cake in a spoke pattern.
In a stainless-steel bowl, beat the cream until it starts to thicken. Add the reduced Moscato d'Asti and beat until soft peaks form. Serve the hazelnut cake with the whipped cream.
Alternative methods of removing those pesky skins from the hazelnuts included bringing 2 cups of water with 2 tablespoons of baking soda to a boil, then adding the hazelnuts for about 2 minutes. I tried this method and was happy with the way the skins came off the hazelnuts after draining them and rinsing them under cold water. For a little added interest, taste, and texture, crush a few of the hazelnuts and incorporate them into the whipped cream prior to serving.