Preheat the oven to 350°F (175°C). Grease and flour a 9×13 inch cake pan.
In a medium bowl, whisk together the all-purpose flour, baking powder, baking soda, and salt. Set aside.
In a large bowl, beat the softened unsalted butter and granulated sugar together until light and fluffy, about 3-4 minutes.
Add the eggs one at a time, beating well after each addition.
Mix in the vanilla extract and yellow food coloring until evenly combined.
Alternately add the dry flour mixture and buttermilk to the butter mixture, beginning and ending with the flour mixture. Mix each addition just until incorporated.
Fold in the mashed ripe bananas gently until evenly distributed.
Pour the batter into the prepared cake pan and spread evenly.
Bake in the preheated oven for 35-40 minutes, or until a toothpick inserted into the center comes out clean.
Remove the cake from the oven and allow it to cool in the pan for 10 minutes.
Transfer the cake to a wire rack to cool completely before serving.