Preheat the oven to 375 degrees F (190 degrees C). Lightly grease four cookie sheets. For the dough, whisk together flour, baking powder, baking soda, cinnamon, and salt in a large bowl until well combined; set aside. Beat together sugars, butter, and shortening in another bowl with an electric mixer until light and fluffy. Add eggs one at a time, beating well after each addition.

Beat in vanilla. Mix in flour mixture until just incorporated. Fold in crushed pineapple, carrot, raisins, and walnuts, mixing just enough to evenly combine. Drop spoonfuls of dough 2 inches apart onto the prepared baking sheets. Bake in the preheated oven until the edges are golden, 10 to 12 minutes. Allow cookies to cool briefly on the baking sheets before removing to a wire rack to cool completely.

For the frosting, beat together cream cheese and butter in a medium bowl with an electric mixer until smooth. Add confectioners’ sugar and pineapple juice; beat until no lumps remain. Spread frosting on cooled cookies. Allow to dry completely before storing. Yields four dozen cookies.