Preheat the oven to 350 F.
In a large bowl, mash the peeled bananas with a fork or whisk. Add the rest of wet ingredients; buttermilk, oil and vanilla extract to the mashed bananas and mix well. Just a whisk work well.
Sift the dry ingredients; flour, baking soda, baking powder and salt in a bowl or directly over the wet ingredients.
Gently fold in to combine. Do not over beat or mix hard.
Add the chopped pineapple pieces and gently fold it in as well.
Line muffin trays with liners or spray with non stick spray. I usually use cupcake liners as they make it easier to store and handle the muffins.
Using a scoop, divide the batter in the muffin tins. Do not overfill the muffin pans. Just fill them until ¾ full.
Bake in the preheated oven for about 17 - 20 minutes. Mine were ready in about 18 minutes. Keep an eye on the muffins and when they appear brown take them out and test it with a tooth pick. The toothpick inserted in the center of the muffin should come out clean without any wet smudges. Few crumbs attached to the toothpick is fine. It should just not be wet.
Cool the banana pineapple muffins in the muffins tin for about 5 minutes and then take it out and cool it entirely on wire racks.