Preheat your oven to 350°F (175°C). Grease a 9x13 inch baking pan.
In a large bowl, whisk together the flour, sugar, baking soda, baking powder, and salt.
In another bowl, mix together the vegetable oil, cooled brewed coffee, applesauce, and vanilla extract.
Pour the wet ingredients into the dry ingredients and mix until just combined.
Pour the batter into the prepared baking pan and spread it evenly.
Bake for 20-25 minutes, or until a toothpick inserted into the center comes out clean.
Remove from the oven and let the cake cool completely in the pan.