Preheat the oven to 350°F (175°C). Grease and flour the 8-inch cake pan. In a large mixing bowl, sift together the flour, spices, salt, and set aside.
In a separate bowl, beat the melted butter and sugar until well combined and slightly creamy, about 2 minutes. Add the eggs one at a time, beating after each addition. Mix in the mashed bananas, crushed pineapple, and vanilla extract until evenly incorporated. Use a spatula to fold in the dry ingredients until just combined.
Pour the batter into the prepared cake pan, smoothing the top with a spatula. Bake in the preheated oven for 40 minutes, or until a toothpick inserted into the center comes out clean and the top is golden brown.
Remove the cake from the oven and allow it to cool in the pan for 15 minutes. Then, transfer to a wire rack to cool completely before frosting.
In a mixing bowl, beat the softened cream cheese, butter, and vanilla until smooth and creamy, about 2-3 minutes. Gradually add the confectioners' sugar, beating until the frosting is fluffy and spreadable. Once the cake is cooled, evenly spread the cream cheese frosting over the top.