Generously grease a 10-inch tube pan with the softened butter, making certain that it is thoroughly coated. Sift together the flour, baking powder, cinnamon, baking soda, and salt.
Break the eggs into a large bowl. Beat vigorously with an electric mixer at high speed until the eggs are light and lemon-colored and have tripled in volume, about 5 minutes. Add the sugar and beat for 3 minutes. Add the mashed bananas, yogurt, and vanilla extract, beating well after each addition. Slowly, fold in the dry ingredients. Pour the batter into the greased pan.
Fill a wok or a large pot with water for steaming and heat until boiling. Place the cake pan in a steamer tray over the boiling water or balance it on a trivet or an empty tuna can in the center of the pan. Cover and steam over high heat for 50 minutes, or until the cake is springy to the touch; check the water level after 30 minutes and add more boiling water if necessary. Remove from the steamer and let cool slightly. Unmold the cake onto a platter, cut into slices, and serve warm with tea. To reheat, steam for 10 minutes.