How to Make It
Preheat the oven to 350° and oil an 8 1/2-by-4 1/2-inch loaf pan. In a large bowl, whisk the flour with the sugar, salt, baking soda and cinnamon. In a medium bowl, whisk the ½ cup of oil with the eggs, bananas, pineapple, pecans and vanilla. Add the dry ingredients to the wet ingredients and whisk until just combined.
Scrape the batter into the prepared pan and bake in the center of the oven for about 1 hour, until a toothpick inserted in the center of the cake comes out clean. Let cool completely, then transfer to a rack.
In a medium saucepan, melt the butter over moderate heat. Add the pineapple and cook, stirring occasionally, until softened, about 5 minutes. Add the confectioners’ sugar and stir until combined. Let cool slightly. Spoon the topping over the top of the cooled cake and let stand until set, about 25 minutes.
In a small bowl, using your hands, blend the confectioners’ sugar with the butter. Add the vanilla extract and milk and whisk until smooth. Using a fork, drizzle the mixture over the top of the cake and let stand until set, about 15 minutes. Slice the cake and serve.