Preheat the oven to 180ºC / 350ºF. Grease and flour a 20cm (8 inch) round pan.
Put the mashed bananas is a bowl. Add the yogurt, eggs, sugar, vanilla extract and cinnamon and mix well.
Sift together the flour, baking powder and salt, and add to the wet ingredients. Mix well. Add the melted butter and mix until well combined.
Pour the batter into the pan and bake for 45 minutes, or until a toothpick inserted in the center comes out clean. Dust with powder sugar before serving.