Preheat oven to 350°F (175°C). Grease an 8-inch baking pan or line with parchment paper.
In a large bowl, whisk together the applesauce, water, oil, vanilla extract, and white vinegar until well combined.
Add the flour, sugar, salt, baking soda, baking powder, and cinnamon directly to the same bowl. Stir until a smooth batter forms. Do not overmix.
Fold in any optional mix-ins (raisins, walnuts, or coconut) if using.
Pour the batter into the prepared pan and smooth the top evenly.
Bake on the center oven rack for 18 minutes, or until a toothpick inserted in the center comes out clean.
Let the cake cool completely before frosting.
For cream cheese frosting: Beat cream cheese and butter together until smooth. Add powdered sugar and vanilla and beat until fluffy. Spread over cooled cake.
Slice into 9 squares and serve. Store leftovers in an airtight container in the fridge for up to 4 days, or freeze individual slices for up to 1 month.