Preheat the oven to 350 degrees F (175 degrees C). Lightly grease and flour a fluted tube pan (such as Bundt).

Combine flour, baking soda, baking powder, and salt in a bowl.

Combine butter and sugar in a blender; process until sugar is almost completely dissolved.

Pour butter mixture into a bowl. Stir in bananas and egg until well blended. Add to flour mixture and stir until just combined. Pour batter into the prepared pan.

Bake in the preheated oven until a knife inserted into the center comes out clean, 30 to 35 minutes.

Remove from the oven and cool in the pan for 10 minutes before inverting the cake onto a plate to serve.