Preheat oven to 350ºF.
Mix together the flour, salt, baking powder, baking soda and nutmeg in a medium bowl—stir lightly with a fork.
Put the oil, melted butter and brown sugar in a bowl. Mix together with a hand mixer, then add the vanilla extract and the eggs, and beat until uniform.
Using a spatula, mix in the bananas and then the pineapple, including its juice.
Add the dry ingredients to the banana mixture and stir with a wooden spoon until barely combined.
Prepare the bundt pan now—brush all its internal surfaces with cooking oil or melted shortening. Then scrape in the batter, level the top, and place it in the preheated oven.
Bake for about 35 minutes or until a cake tester comes out entirely clean.
Let it stand on a rack for about ten minutes. Then gently slide a thin knife around the edges to loosen it a bit, being careful not to harm the bread, and turn it out onto the rack.
Let it cool completely.
Make the glaze. Sift the powered sugar through a sieve into a small bowl. Add 3 tablespoons of the milk and the vanilla and then whisk together until everything is completely smooth and non-bumpy. Add more milk if it seems too thick. Spoon it on top of the cooled bread, let it harden and you are ready to go.