Place yogurt in a strainer lined with a coffee filter and set over a bowl. Refrigerate for at least 40 minutes to allow liquid to drain. Discard liquid and set yogurt aside.

Preheat the oven to 350 degrees F (175 degrees C).

Combine gingersnap cookies, amaretti cookies, and butter in a bowl; mix well. Press crust into the bottom of a 9-inch springform pan.

Bake in the preheated oven until golden, about 12 minutes.

Remove crust from oven and reduce temperature to 325 degrees F (165 degrees C). Let crust cool completely.

While crust cools, beat cream cheese, sugar, vanilla extract, cinnamon, ginger, cardamom, and salt together in a mixing bowl using an electric mixer until well blended. Add eggs 1 at a time, beating on low speed and scraping the sides of the bowl after each addition. Stir in yogurt. Pour filling into the cooled crust.

Bake in the preheated oven until cake is set on sides but slightly shimmers in center, about 50 minutes.

Let cool completely and remove from pan. Serve with caramel sauce.