Preheat oven to 350ºF (180°C).
Grease (use shortening not butter) and flour a 10-cup capacity or large 12-cup Bundt pan.
Sift together 2 ½ cups all-purpose , 2 ½ teaspoons baking powder, and ½ teaspoon salt.
In a large mixing bowl with an electric mixer or the bowl of a stand mixer, beat ¾ cup unsalted butter until creamy, about 1 minute.
Add 1 cup white sugar and ½ cup brown sugar gradually, beating for 2 more minutes until light.
Add 3 eggs, one at a time, beating well after each addition, and beating an additional 1 minute after the last one is incorporated.
Add ½ teaspoon vanilla extractextract and mix.
Add dry ingredients in 3 parts, alternating with 1 ¼ cups buttermilk in 2 parts. That means you start and end with dry ingredients.
Add 1 cup mashed bananas and mix just until no streaks of flour remain.
Pour batter into the prepared pan and bake in the middle rack for 45-50 minutes, until the top is golden brown and a cake tester or toothpick comes out clean. Time might differ depending on the oven and pan used.
Cool in a wire rack for about 15-20 minutes, carefully invert onto a plate, invert it again onto the wire rack and let cool completely. If the cake at first resists, shake the pan up and down carefully or let it cool down a little more, and try again.
Let cool completely, glaze and let it dry before you cut it into individual slices.
Store leftover cake for a day at room temperature, covered in plastic wrap and then refrigerate or freeze.