Line a 15x10x1-inch baking pan with foil, allowing foil to extend over short edges of pan; grease foil and set aside. In a medium bowl, combine flour, baking powder and salt; set aside. In a large mixing bowl, beat 1 cup butter with an electric mixer on medium to high for 30 seconds. Add 1-1/4 cups granulated sugar; beat until combined. Beat in egg, lemon peel, lemon juice and vanilla until combined. Beat in as much of the flour mixture as you can with the mixer. Using a wooden spoon, stir in any remaining flour mixture. Spread dough into prepared pan.
In a small bowl, combine 1 tablespoon granulated sugar and cinnamon. Sprinkle cookie crust with cinnamon-sugar mixture. Bake in a 350 degree F oven for 20 to 25 minutes or until golden and edges are lightly browned. Place pan on a wire rack. Cool cookie completely in baking pan. Use foil to remove from pan and break cookie crust into about 24, 2- to 3-inch irregular shapes.
Lightly butter and sugar a 9x9x2-inch baking pan or 9x1/2-inch round cake pan. Place nectarines, cut side up, in the cake pan. In a small bowl, combine sweet wine, brandy and vanilla. Pour the wine mixture over nectarines. Sprinkle 1/4 cup granulated sugar over the fruit and dot with 1 tablespoon butter. Cover the pan with foil. Bake in a 300° oven 15 to 20 minutes or until the fruit is tender, but still holds a shape. Remove from oven.
To serve, place the warm nectarines in a shallow dessert bowl. Scoop the Honey Ginger Ice Cream on top. Arrange a few of the broken cookie pieces in the bowls.* Dust with powdered sugar. Makes 4 servings.
Place remaining cookie pieces in an airtight container and freeze up to 1 month. Thaw cookie pieces before using. Use to make this recipe again or for another use.