Preheat oven to 350 degrees F. Grease a 9-inch cake pan.
Make the apple cardamom cake batter. Whisk together vegetable oil with eggs, Greek yogurt, and vanilla until smooth.
In a separate bowl, combine the flour with sugar, cinnamon, baking powder, baking soda, salt, and cardamom. Add the wet ingredients to the flour mixture, stirring just until combined. Fold in the chopped apples and pour the batter into the prepared cake pan.
Make the cinnamon-sugar streusel. Combine sugar with cinnamon, cardamom, and melted butter until well combined. Sprinkle the streusel on top of the cake.
Bake the cake for 40-45 minutes or until a toothpick inserted in the center comes out clean. Remove the cake from the oven and let cool completely on a wire rack.
Meanwhile, make the pistachio cream. In a food processor, grind the pistachios until smooth, about 5 minutes. Add the powdered sugar and process until combined. Add water and process and until smooth and thick, another 1-2 minutes. Add heavy cream and process until creamy and thick, about 5 minutes. Chill the pistachio cream until ready to serve. The cream will thicken as it chills.
Notes
You can make the pistachio cream up to 2 days ahead of time.Use apples that hold their shape even after baking, such as Granny Smith, Honeycrisp, Pink Lady, and Braeburn.