Preheat the oven to 325 F. Lightly coat three 9-inch round cake pans with cooking spray, then line the bottoms of the pans with parchment paper and lightly spray with oil.
In a large bowl, combine the flour, sugar, baking soda, cinnamon, rose petals, and cardamom and mix well. In a medium bowl, lightly whisk the eggs with vegetable oil, coconut oil, vanilla, and salt, then stir in the dry ingredients, mixing just until they are moistened. Stir in the sour cream. Using a large spatula, fold in the crushed pineapple and juice, bananas and pecans. Divide the batter evenly between the prepared pans.
Bake the cakes in the centre of the oven for 45 minutes, rotating the pans after 20 minute, until the cakes are golden brown and cake tester comes out clean in the middle. Let the cakes cool in the pans on a wire rack for 20 minutes. Place a rack over each pan, invert the cakes onto the racks and remove the pans. Peel off the parchment paper. Cool completely.
Meanwhile, in the bowl of a stand mixer fitted with a paddle attachement, beat the cream cheese and butter on medium high speed until smooth. Sift the powdered sugar into the bowl, beating until smooth. Beat in the orange zest and vanilla paste.
Using a bread knife, trim the domed tops of the cakes so they are flat. Set one layer on a cake stand and spread with the frosting. Continue to stack and frost the layers, then spread a thin layer of frosting all over the cake as the base coat.
Refrigerate for 15 minutes, until set. Spread the remaining frosting evenly over the sides and top of the cake. Decorate the outer circumference of the top of the cake with whole pecans and rose petals. Slice and serve.