Preheat oven to 350°F (180°C). Grease three 8-inch round cake pans and line with parchment paper.

Wet Ingredients: In a large bowl, beat together eggs, granulated sugar, brown sugar, oil, buttermilk, and vanilla. Mix in mashed banana and drained pineapple until combined.

Dry Ingredients: In a separate bowl, whisk together flour, baking powder, baking soda, cinnamon, allspice, and salt.

Combine: Add dry ingredients to wet ingredients and mix just until incorporated. Fold in chopped pecans (or use the on the outside of the cake frosting).

Bake: Divide batter evenly between pans. Bake on the center rack for 28–35 minutes, or until a toothpick inserted in the center comes out clean. Cool in pans for 10–15 minutes, then turn out onto wire racks to cool completely.

Cream Cheese Frosting: Beat cream cheese and butter together until smooth. Mix in vanilla. Add powdered sugar, one cup at a time, until desired consistency is reached. Beat until smooth and fluffy.

Assemble: Place one cake layer on a serving plate. Spread about 1/2 cup frosting evenly on top. Repeat with remaining layers. Frost the sides of the cake and garnish with chopped pecans, if desired. Chill cake for at least 30 minutes before serving.