In a large bowl, cream together the butter, sugar, and cream cheese until light and fluffy. Beat in the egg and vanilla. Combine the flour, dry pudding mix, baking powder, and salt; stir into the creamed mixture. Cover dough, and refrigerate for at least one hour for easier handling.
Preheat oven to 350 degrees F (175 degrees C). Grease cookie sheets. Shape teaspoonfuls of dough into finger shapes, about 1 1/2 inches long. Place cookies on prepared cookie sheets.
Bake for 9 to 12 minutes in the preheated oven, or until set and very lightly browned on bottoms. Cool completely on a wire rack.
In small saucepan over low heat, melt together chocolate and shortening, stirring constantly until smooth and well blended. Drizzle a small amount of chocolate over each cookie. Allow the chocolate to set before storing.
