Preheat the oven to 350 degrees.
Melt one tablespoon of butter in a small bowl, then use a pastry brush to spread the butter all over the bundt pan. Add a tablespoon of flour to the pan and shake it to evenly coat the inside.
In a medium bowl, whisk together the flour, baking powder, baking soda, cinnamon, and salt. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment, beat the butter and sugars on medium-high speed for 3-4 minutes until light and pale in color.
Add the mashed banana and mix until fully combined.
Add the eggs, beating between with each addition, then scrape the bowl down with a rubber spatula.
In a large measuring cup, mix the yogurt and vanilla together.
Alternate adding the dry ingredients and the yogurt to the batter until everything is mixed in.
Scrape the bottom of the bowl with a rubber spatula to ensure everything is evenly incorporated.
Transfer the batter into the prepared bundt pan and smooth out the top with the rubber spatula.
Bake the cake for about 42 minutes or until a skewer inserted comes out clean.
Allow the cake to cool in the pan for 5 minutes, then use a knife to loosen it from the sides and immediately turn out onto a cooling rack.