In a medium mixing bowl with an electric mixer, beat butter on medium speed for 30 seconds. Add the 1-3/4 cups powdered sugar; beat until combined, scraping bowl. Beat in egg. In a small bowl combine flour and cornstarch; add to butter mixture. Beat until combined. Stir in finely ground walnuts. Divide the dough in half. Cover and chill for 2 to 3 hours or until firm.
On a lightly floured surface, roll half of the dough at a time to 1/8-inch thickness. (Keep remaining dough chilled in the refrigerator until ready to use.) Cut out cookies with a 3-inch star-shaped cookie cutter. Cut out a smaller star from center of half of the cookies. Place cookies on an ungreased cookie sheet. Bake in a 325 degree F oven for 12 to 14 minutes or until very lightly browned. Cool on a wire rack. Carefully spread the solid star cookies with raspberry preserves. Sift powdered sugar over the cookies with star cutouts; place them on top of the preserves. Makes about 30 cookies.