For the banana cake: Preheat the oven to 350 degrees F. Grease and flour a 9-inch round cake pan.
In the bowl of an electric mixer, combine the butter, brown sugar and granulated sugar. Mix on medium-high speed until light and fluffy, about 5 minutes.
Meanwhile, sift the flour, baking soda, baking powder, cinnamon and salt into a medium bowl. Set aside.
Add the bananas to the butter mixture and mix until combined. Let the mixer do the work of mashing for you. Add the eggs one at a time and mix until well combined. Mix in the yogurt and vanilla. Turn the mixer to low and add the dry ingredients until just combined. Do not overmix.
Pour the batter into the prepared cake pan. Bake until a cake tester or toothpick comes out clean, 45 to 50 minutes. Cool in the pan for 5 to 10 minutes, then turn onto a wire rack and cool completely.
For the cream cheese frosting: Using the electric mixer on high speed, blend the cream cheese and butter until light and fluffy, 4 to 5 minutes. With the mixer on low, add the confectioners' sugar and then the vanilla.
Spread the frosting on top of the cake. Decorate around the perimeter of the cake with raspberries, if desired.
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