Preheat the oven to 350° F. Butter and flour your bundt cake pan(s).
In a mixing bowl, whisk together the flour, sugar, salt, and baking soda. Make a well in the center of the dry ingredients. In a separate bowl, combine eggs, bananas, oil, undrained pineapple, and vanilla; add all at once to dry ingredients, stirring until well moistened. This can also be done in a stand mixer if you wish.
Pour batter into the prepared pan(s); using a pastry bag makes this neater, but is certainly not necessary. Bake for about 35 minutes for mini Bundt cakes or 65 to 70 minutes for a large Bundt cake. Cool in pan 15 minutes, then remove and cool on wire rack. Sprinkle with powdered sugar and enjoy.
This recipe makes 12 mini Bundt cakes or one 10-inch Bundt cake. Remember that a full-size Bundt cake will take longer to bake: 65 to 70 minutes for a large Bundt cake (instead of 35 minutes for mini Bundt cakes).