Sift flour and next 3 ingredients together onto parchment paper. Beat corn syrup and next 3 ingredients in a large bowl at medium-high speed with an electric mixer 1 to 2 minutes or until well blended. Add eggs, 1 at a time, beating just until combined. Add flour mixture gradually, using a dough hook or working by hand. Divide dough into 4 equal parts, wrap each in plastic wrap, and place in airtight container; chill overnight.
Preheat oven to 350°. Grease flat work surface lightly with shortening. Cut parchment to fit baking sheet, smooth onto greased surface, and flour well. Lightly flour rolling pin and dough.
Roll 1 quarter of dough to a thickness of 1/8 inch. (To ensure even thickness, lay rulers beside dough as shown--close enough for both ends of rolling pin to "ride" on rulers.) Arrange pattern templates on dough, spacing at least 1/2 inch apart. Cut with sharp knife or pizza cutter. (Gingerbread will rise slightly during baking, so windows, doors, etc., may fill in slightly.) Repeat process with remaining dough until all templates are cut. Wrap dough that is not being used or baked with plastic wrap.
Slide parchment and cutouts onto ungreased baking sheet, and bake 15 minutes. (For crisp, straight edges, recut misshapen pieces as soon as removed from oven.) Let cool 5 minutes on wire rack. Using a wide spatula, lift gingerbread cutouts off parchment, arrange on flat surface, and cool to room temperature.
Note: If cutouts don't lie flat as they cool, they will warp and make the cottage difficult to assemble. Store cooled, baked pieces on a flat, cool, dry surface. Do not stack or layer.