Heat the oven to 325°F.
In a large bowl, combine the mashed bananas, eggs and oil. In a separate bowl, combine the flour, sugar, pudding mix, baking soda and salt. Add the dry ingredients to the wet ingredients and combine well but gently (I swear this came out differently when I used an aggressive electric mixer). Fold in the coconut and chocolate chunks.
Grease and flour a Bundt pan. Pour the batter into the pan. (This can also make two 8- by 4-inch loaves, but it’s so much more moist in one Bundt pan!)
Bake until the cake springs back when lightly pressed and a toothpick inserted in the center comes out clean, 60 to 80 minutes. (Test it with a toothpick at around 50 minutes.) Let it cool slightly in the pan, then use a butter knife to gently release the cake from the sides of the pan and around the inner circle, then flip it onto a plate.
Let it cool, and cut it into slices. Rewarm them and serve them with salty butter!