Preheat oven to 350°. Beat butter and sugar at medium speed with an electric mixer 2 minutes or until light and fluffy. Add egg and lemon zest; beat until smooth.
Combine flour and next 3 ingredients; gradually add to butter mixture, beating just until blended. Shape dough into 2 balls, wrap in wax paper, and chill 1 hour.
Roll dough out onto a lightly floured surface to 1/8-inch thickness. Cut into shapes using a 3-inch star-shaped cutter. Cut centers out of half of cookies with smaller star-shaped cutters. Place on greased or parchment paper-lined baking sheets. Bake, in batches, 10 to 12 minutes or until edges are lightly browned; cool on wire racks.
Spread whole cookies evenly with a thin layer of jam. Sprinkle cut-out cookies with powdered sugar. Place 1 cut-out cookie on top of each whole cookie.
Star Cookies: To make these patriotic cookies (which can be used to garnish our Celebration Cupcakes), start with the Jam Stars recipe. Roll out dough to 1/4-inch thickness; cut with a 2-inch star-shaped cookie cutter. Place on baking sheet, and insert a short wooden skewer halfway into side of each cookie. Bake as directed.
Meanwhile, combine 4 cups powdered sugar, 6 tablespoons half-and-half, and 1/4 teaspoon vanilla extract, stirring with a whisk until icing is smooth. Divide into batches, and tint with desired amount of red or blue food coloring. Spoon icing onto cooled cookies, and spread to edges.