Preheat the oven to 375 degrees F (190 degrees C). Grease cookie sheets. Sift together the flour, baking powder, baking soda, salt and cardamom. Set aside.
In a medium bowl, cream together the butter, sugar, cream cheese and almond paste until smooth. Beat in the egg, vanilla and lemon zest. Gradually blend in the dry ingredients until well mixed. Drop by spoonfuls onto the prepared cookie sheets.
Bake for 8 to 10 minutes in the preheated oven. Allow cookies to cool on baking sheet for 5 minutes before removing to a wire rack to cool completely.