Preheat your oven to 350°F (175°C).
Grease and line a 9x13-inch baking pan with parchment paper.
In a large bowl, whisk together the flour, granulated sugar, light brown sugar, cocoa powder, baking powder, baking soda, and salt.
In another bowl, mix the applesauce, yogurt, buttermilk, melted coconut oil, and vanilla extract until smooth.
Add the wet ingredients to the dry ingredients, mixing until just combined.
Pour the batter into the prepared pan and spread it evenly.
Bake for 30-35 minutes, or until a toothpick inserted into the center comes out clean.
Allow the cake to cool in the pan for 10 minutes, then transfer to a wire rack to cool completely.