Lightly spoon flour into dry measuring cups; level with a knife. Combine flour, baking soda, salt, and cinnamon, stirring well with a whisk.
Place granulated sugar and butter in a large bowl; beat with a mixer at high speed until light and fluffy. Add egg substitute; beat until well blended. Beating at low speed, gradually add flour mixture; beat just until a soft dough forms. Divide dough into 2 equal portions, and wrap each dough portion in plastic wrap. Chill at least 1 hour.
Preheat oven to 375°.
Roll each dough portion into a 1/8-inch thickness on a lightly floured surface; cut with a 2-inch square cookie cutter with fluted edges to form 32 cookies. Repeat procedure with remaining dough portion. Place cookies 1 inch apart on parchment-lined baking sheets. Cut out centers of 32 cookies with a 1-inch square cookie cutter with fluted edges. Bake cookies at 375° for 10 minutes or until edges are lightly browned. Cool on pans 5 minutes. Remove from pans; cool completely on wire racks.
Spread center of each whole cookie with about 1/2 teaspoon jam. Sprinkle cut-out cookies with powdered sugar. (A) Place 1 cut-out cookie on top of each whole cookie.