Into a large bowl, sift together flour, baking soda, and spices. In a medium bowl with electric mixer beat cream until it just slightly holds stiff peaks. In another large bowl beat butter and sugar until mixture is light and fluffy. On low speed, beat in the corn syrup and whipped cream, beating until cream is just combined. Add flour mixture and beat until combined well. Form dough into a log. Chill log, wrapped in plastic wrap, until firm, at least 2 hours, and up to 2 days.
Preheat oven to 400 degrees F.
Cut dough into quarters and work with 1 quarter at a time, keeping remaining dough covered and chilled. Using a rolling pin dusted with flour, roll out dough into a round on a floured pastry cloth, rolling dough as thin as possible (less than 1/8" thick and about 14" in diameter) and with assorted 2" to 3" cutters cut out cookies. Carefully transfer cookies as cut to ungreased baking sheets with a metal spatula, arranging them about 1/2" apart, and top each with an almond slice. Reroll scraps and cut out more cookies in same manner.
Bake cookies in batches in upper and lower thirds of oven, switching position of sheets halfway through baking, until cookies puff and then collapse slightly, about 6 minutes. Cool cookies on sheets 1 minute and transfer with metal spatula to racks to cool completely. Make more cookies with remaining dough in same manner. Cookies keep in airtight containers at room temperature 1 week.