1. Preheat your oven to 350°F. 
2. In a large mixing bowl, whisk together the flour, sugar, baking powder, baking soda, cinnamon, ginger, and salt. 
3. Add in the vegetable oil, applesauce, non-dairy milk, and vanilla extract. Mix until fully combined. 
4. Fold in the grated carrots and chopped walnuts (if using). 
5. Pour the batter into a greased 9x13 inch baking pan. 
6. Bake for 30-35 minutes, or until a toothpick inserted into the center comes out clean. 
7. Allow the cake to cool before slicing and serving. Enjoy!