Preheat oven to 350F. Butter a nonstick bundt cake pan. If not using a nonstick pan, butter then dust with flour and pat out the excess over sink.
Evenly spread out the chopped pecans on a sheet pan. Toast in the oven for 4-5 minutes, until smells nutty and lightly browned. Let cool completely.
In a large bowl, combine the flour, baking powder, baking soda, ground cinnamon, salt, and ground nutmeg. Mix well, then set aside.
In the bowl of a stand mixer fitted with the whisk attachment, combine the eggs and olive oil. Beat for 1-2 minutes, until light and foamy.
Add the granulated cane sugar and packed light brown sugar to beat 2-3 minutes, until very frothy.
Add the vanilla extract, mashed bananas, toasted pecans, sour cream, and crushed pineapple. Mix until well combined.
Add in the flour mixture then mix JUST until combined. Over mixing the batter can cause a dense cake.
Bake in the middle oven rack for 45-60 minutes, until top is cracked and set, and a toothpick inserted into the center comes out with only moist crumbs.
Let cool in the pan for 20 minutes then flip over onto a baking rack to cool completely.