Position a rack in the center of the oven and preheat the oven to 350˚F. Spray two 8-inch round pans with nonstick spray or butter them generously.
Into a medium bowl, sift together the flour, baking powder, baking soda, and salt.
In a separate medium bowl, whisk together the bananas, yogurt, and oil until smooth.
In the bowl of an electric mixer fitted with the paddle attachment, beat together the sugar and butter on medium-low speed until the mixture looks like dampened sand, about 1 minute.
Add the eggs one at a time, giving the first about 30 seconds to incorporate before adding the second. Increase the speed to medium-high, beating until light in texture and much paler in color, 4 to 5 minutes (don’t skimp on the beating time, here—the significant change in color will be your cue that the sugar has begun to dissolve). Beat in the vanilla extract.
Reduce the mixer speed to low. Stir in the dry ingredients and banana-yogurt mixture in five alternating additions, beginning and ending with the dry ingredients, letting each addition fully absorb into the batter before adding the next. Finish folding the batter gently by hand to ensure it is well blended.
Divide the batter into two prepared pans and smooth the tops. Bake until a toothpick comes out clean, 20 to 25 minutes. Cool the cakes for 10 minutes in the pan, then invert onto a wire rack. To cool completely.
Place one cake on a stand or platter. Cover only the top with half of the frosting and smooth it flat. Place the second cake onto the first and spread the remaining frosting over the top of the cake. Serve at once or wrap loosely in plastic and chill for up to two days. Serve at room temperature for rmaximum flavour.
One of the tricks of using coconut sugar successfully in baking is to find a recipe that has plenty of tenderizing, moisture-lending ingredients in it—such as mashed bananas or other fruit purees, oils, and buttermilk or yogurt—as coconut sugar tends to dry out baked goods.