Set your oven to 300°F or 149°C). Line a baking sheet with parchment paper.
Spread pecans on a baking sheet and toast for 7–8 minutes, until fragrant and lightly browned. Cool completely.
Increase the oven's temperature to 350°F (around 177°C). Grease and flour a 10- to 12-cup bundt pan.
In a bowl, combine the flour, baking powder, baking soda, salt, allspice, and cinnamon, giving it a good whisk.
Whisk together eggs, oil, pineapple juice, and sour cream. Add sugars and vanilla; whisk them until smooth. Fold in banana, pineapple, and most pecans.
Gently fold wet ingredients into dry ingredients until just combined.
Add the batter to the pan. Bake for 1 hour or until a toothpick inserted in the middle comes out clean or with just a little moisture.
Cool in pan for 1 hour. Invert onto a wire rack and cool completely.
Beat butter and cream cheese until smooth. Gradually add vanilla, sugar, and 2 tablespoons milk; beat until light and fluffy. Add cinnamon (optional). Add more milk if needed.
Once the cake is cool, frost it with icing and sprinkle with the remaining pecans.