Line 2 heavy large baking sheets with parchment paper. Using an electric mixer, beat the butter, sugar, vanilla, and salt in a large bowl until fluffy. Beat in the egg. Add the flour and mix just until a dough forms.
Fit a pastry bag with a large star tip, and fill the pastry bag with the cookie dough. Pipe the dough onto the prepared baking sheets into stars, spacing 1-inch apart. If desired, press about 4 miniature chocolate chips into the center of each star at this point. Bake the cookies until they are pale golden around the edges and on the bottom, about 15 minutes. Cool the cookies for 5 minutes. Using a metal spatula, transfer the cookies to a rack and cool completely.
When the cookies have cooled, spoon approximately 1/4 teaspoon of preserves atop the flat side of 1 cookie. Press a second cookie onto the preserves. Repeat with the remaining cookies and preserves. (Can be made 2 days ahead. Store between sheets of waxed paper in an airtight container at room temperature.)
Cook's Notes: Alternately, the cookies can be made into thumbprint cookies. To do so, refrigerate the dough until it is cold, about 2 hours. Roll 2 teaspoons of dough for each cookie into 1-inch-diameter ball. Place the cookies on the baking sheets, spacing 2 inches apart. Make a deep indentation in the center of each cookie by pressing the back of a teaspoon into the cookies. Fill each indentation with 1/2 teaspoon of strawberry or raspberry preserves or chocolate chips, and bake as directed.
A chilled chocolate ganache may be used in place of the preserves to fill the indentations in these cookies. To do this, do not fill the indentations before baking the cookies. While the cookies bake, make the ganache by mixing equal parts of warm cream and chocolate until the chocolate melts and the mixture is smooth, then chill the ganache. Once the cookies have baked and cooled, and the chocolate ganache is cold and firm but still spreadable, spoon or pipe the chilled ganache into the empty indentations on the cookies.