In a bowl, whisk together flour, cornstarch, baking powder, baking soda, cardamom, cinnamon, ginger, nutmeg, and salt.
In a large bowl, cream together butter and sugars until light and fluffy. Gradually beat in the eggs.
Beat in half of the flour mixture to the wet ingredients.
Add the sour cream and oil. Mix until just combined.
Stir in the rest of the flour mixture.
Grease and flour the springform pans. Divide the batter between the pans and bake for 25-30 minutes each. Let the cake cool for a few minutes before transferring to a wire rack to cool completely.
Meanwhile, whisk together the cream cheese and powdered sugar for the frosting.
Place one cake layer on a serving plate and spread some of the frosting on top. Top with the second cake layer and spread the remaining frosting over the top and sides of the cake.
Notes
If need be, you can also bake the cake layers one after the other.