Preheat your oven to 350°F (175°C).
Grease and line a 9x13-inch baking dish with parchment paper.
In a large bowl, whisk together the flour, granulated sugar, baking powder, baking soda, and salt.
In another bowl, mix the dairy-free buttermilk, melted coconut oil, dairy-free yogurt, and vanilla extract until smooth.
Add the wet ingredients to the dry ingredients, mixing until just combined.
Pour the batter into the prepared baking dish and spread it evenly.
Bake for 25-30 minutes, or until a toothpick inserted into the center comes out clean.
Allow the cake to cool in the pan for 10 minutes.