Preheat the oven to 350°F. Grease and flour a 9x13-inch baking pan.
In a large mixing bowl, whisk together the flour, sugar, baking powder, baking soda, cinnamon, nutmeg, ginger, and salt until well combined.
In another bowl, mix the applesauce, vegetable oil, eggs, and vanilla extract until smooth.
Pour the wet ingredients into the dry ingredients and stir until just combined. If using, fold in the chopped pecans and raisins.
Pour the batter into the prepared baking pan and spread it evenly. Bake for 30-35 minutes, or until a toothpick inserted into the center comes out clean.
While the cake is baking, prepare the glaze by whisking together the powdered sugar, milk, and vanilla extract in a small bowl until smooth.
Once the cake is done, remove it from the oven and let it cool in the pan for about 10 minutes. Drizzle the glaze over the warm cake before serving.