Preheat oven to 350 degrees. Generously grease and flour bottom and sides of a Bundt pan.
Soak diced apples in mixture of 2 cups water and 2 tablespoons fresh lemon juice.
In a large bowl combine sifted fl our, sugars, baking soda, salt, cinnamon, ginger, and nutmeg. Add vanilla, oil, and eggs, mixing well. Add soaked apples, but do not drain; instead, spoon apples into batter so that some of the soaking liquid is included for moistness. Fold in the nuts.
Bake on low oven rack for 1 1/4 hours or until toothpick inserted into cake comes out clean. Cool cake in pan for 10 minutes.
For the Glaze
Combine first 4 ingredients in a small heavy-bottom saucepan. Cook over medium heat, stirring constantly, until slightly thickened, about 3 or 4 minutes. Remove from heat, let cool for 5 minutes, and then stir in the vanilla.
Pour glaze over cooled cake and decorate with pecan halves.