To prepare cake: Rub butter generously on bottom and sides of a Bundt cake pan. Add flour and turn to coat all surfaces. Preheat oven to 325 degrees. Combine apples with 2 cups water and lemon juice. Set aside. In a large mixing bowl, sift together granulated and brown sugars, 3 cups sifted flour, baking soda, salt, cinnamon, ginger and nutmeg. Add vanilla, oil and eggs; mix well. Spoon soaked apples into batter, so that some of the soaking liquid is included for moistness. Fold in nuts. Bake on low oven rack for 1 hour, 15 minutes or until a toothpick inserted into the cake comes out clean. Cool cake in pan 10 minutes, then turn out onto cake rack. When cake has cooled, prepare glaze: In a small saucepan with heavy bottom, combine butter, granulated sugar, brown sugar and cream. Cook over medium heat, stirring constantly, until slightly thickened, about 3 to 4 minutes. Remove from heat; let cool 5 minutes. Stir in vanilla. Pour glaze over cake. Garnish as desired with nut halves. Yield: 12 to 16 servings.