Preheat the oven to 350°F.

Lightly oil three 8-inch round cake pans, then line the bottom of each pan with parchment paper.

In a large mixing bowl, stir the water and flaxseed together. Set the mixture aside while you combine the dry ingredients. It will need to sit for at least 5 minutes for the flaxseeds to gel.

In a large mixing bowl, whisk together the flour, baking powder, baking soda, cinnamon, and salt. Set this aside.

Stir the banana, pineapple, oil, and vanilla together in a medium mixing bowl. Set this aside.

Add the sugar and brown sugar to the bowl with the flax mixture. Beat the ingredients together using an electric mixer at high speed for one minute, until the mixture is slightly foamy.

Add the banana mixture to the flax mixture. Stir everything together by hand. The ingredients may not combine completely at this stage, which is fine.

Begin stirring the flour mixture into the flax and banana mixture. Add the flour mixture in about three increments, stirring each in just until combined.

Fold the pecans into the batter.

Transfer the batter to the prepared baking pans, distributing it as evenly as you can.

Place the baking pans into the oven. Bake the cake layers for 26 to 30 minutes, until a toothpick inserted into the center comes out clean.

Place the cake pans on cooling racks when you take them out of the oven. Let the cake layers cool completely.

Once they're cool, carefully invert one of the layers onto a cake dish, then remove the parchment paper (Note 2).

Slather the top of the cake layer with frosting, then carefully remove a second layer from the pan and place it over the first layer. Slather the second layer with frosting, then place the third layer on top. Cover the top and sides of the cake with frosting. Optionally, garnish the cake with pecan halves.

Slice the cake and serve.