Preheat oven to 325 degrees F (165 degrees C). Grease a large tube pan with cooking spray. Line with parchment paper; spray parchment paper.
Whisk all-purpose flour, almond flour, baking powder, cardamom, and salt together in a bowl.
Combine sugar, cream cheese, and butter in a bowl; beat with an electric mixer until light and fluffy. Add rose water and vanilla extract. Add 1 egg at a time, beating well after each addition. Beat in flour mixture gradually on low speed until batter is smooth and no lumps remain.
Pour batter into the prepared tube pan.
Bake in the preheated oven until a toothpick inserted into the center comes out clean, 50 to 60 minutes. Cool in the pan for 15 minutes. Invert onto a wire rack to cool completely before slicing.