Preheat oven to 350°F. Grease two 8 or 9-inch round cake pans and set aside.
In a medium bowl, whisk the flour, cinnamon, baking powder, baking soda, salt, and nutmeg together. Set aside.
Using a hand mixer or a stand mixer fitted with the paddle attachment, cream the butter with both sugars until smooth. Add the crushed pineapple, mashed banana, yogurt and vanilla extract and beat to incorporate. Add the dry ingredients and mix on low speed until just combined.
Divide the batter evenly between the two pans. Bake for 38-40 minutes, or until a toothpick inserted into the center comes out clean. Allow the cakes to cool in the pans for 15 minutes before transferring to a wire cooling rack to cool completely.
To make the cream cheese frosting:
Using a hand mixer or a stand mixer fitted with the paddle attachment, beat the cream cheese and the butter until smooth and creamy, about 5 minutes. Add the powdered sugar and beat to combine.
To assemble the cake:
Use a large serrated knife to level the top of each cake, if necessary, to create a completely flat surface. Place one layer on your cake stand and spread ¾ cup of frosting evenly on top. Position the second layer on top and evenly cover the top and sides with the remaining frosting.