In a large mixing bowl beat butter and shortening with an electric mixer on medium to high speed for 30 seconds. Add the 3/4 cup sugar, the baking powder, and salt. Beat until combined, scraping sides of bowl occasionally. Beat in egg, milk, and vanilla. Beat in as much of the flour as you can with the mixer. Using a wooden spoon, stir in any remaining flour.
Divide dough in half. Cover and chill the dough for 3 hours or until it is easy to handle.
For filling, in a small mixing bowl stir together cream cheese and the 2 tablespoons sugar. Stir in the coconut. Set aside.
On a lightly floured surface, roll half of the dough at a time into a 10-inch square. Using a fluted pastry wheel or a sharp knife, cut square into sixteen 2-1/2-inch squares. Place squares 2 inches apart on an ungreased cookie sheet. Cut 1-inch slits from each corner toward the center of each square. Spoon a level teaspoon of the filling in each center. Fold every other tip to center to form a pinwheel, pressing lightly to seal the tips. Carefully sprinkle some of the chopped nuts onto the center of each pinwheel; press nuts lightly into the dough. If desired, sprinkle cookies with colored sugar.
Bake in a 350 degree F oven for 8 to 10 minutes or until edges are lightly browned. Cool for 1 minute on cookie sheet. Transfer cookies to a wire rack; cool. If desired, drizzle cooled cookies with Pineapple Icing and sprinkle with additional colored sugar. Makes 32 cookies.
In a small mixing bowl, stir together 3/4 cup sifted powdered sugar and enough pineapple juice (about 1 tablespoon) to make icing of drizzling consistency.