In a large bowl, whisk together the flour, granulated sugar, light brown sugar, baking powder, baking soda, and salt.
In another bowl, mix the mashed bananas, dairy-free yogurt, dairy-free buttermilk, melted coconut oil, and vanilla extract until smooth.
Add the wet ingredients to the dry ingredients, mixing until just combined.
Pour the batter over the banana layer in the cake pan, spreading it evenly.