Grease several baking sheets or coat with nonstick spray.
In a medium bowl, thoroughly stir together the flour, salt, baking soda and set aside. In a large bowl, with electric mixer on medium speed, beat together sugar, butter and shortening until well blended and fluffy, about 2 minutes.
Add the eggs, vanilla, corn syrup and lemon extract and beat until evenly incorporated. Beat in half of the flour mixture, just until well blended and smooth. Let the dough stand to firm up for about 5 minutes. Using a scant 1/4 cup measure of dough, shape into balls with lightly greased hands. Place on the baking sheets, spacing about 3/4" apart.
Using your hands press and pat the balls to about 3 1/4" in diameter.
Bake the cookies one sheet at a time, in the middle of the oven for 10-14 minutes, or lightly browned at the edges and tops just spring back when lightly pressed in the centers.
Reverse the sheet from front to back halfway through baking to ensure even browning.
Transfer the sheet to a wire rack and let stand until the cookies firm up slightly -- 1-2 minutes.
Using a spatula, transfer the cookies to wire racks.Let stand until completely cooled.
FOR THE FONDANTS:
in a medium, heavy saucepan, bring 1/2 cup water and the corn syrup just to a boil over medium-high heat. Remove from heat and stir in powdered sugar and vanilla until completely smooth. Place the chocolate in a small deep bowl. Pour 2/3 cup of hot vanilla fondant over the chocolate, stir until chocolate is partially melted. Pour another 1/2 cup of vanilla fondant over the chocolate. Stirring constantly, thin the chocolate fondant to a fluid, but not runny consistency -- by adding 3-4 tsps of hot water, a little at a time. Stir until the chocolate melts completely and the water is incorporated. Set the wire racks with cookies over wax paper to catch drips. Using a small wide bladed spatula, spreader etch.immediately ice half of each cookie with chocolate fondant.)if fondant stiffens as you work, thin it by thoroughly stirring in a few drops of hot water. It it cools completely, rewarm it over low heat, stirring. If necessary, adjust the consistency of vanilla fondant by stirring in additional powdered sugar or hot water until fluid, but not runny. Ice the second half of each cookie with vanilla fondant. Let cookies stand until the icing sets.at least 2 hours, preferably 4 hours. Store them in a single layer or layered between wax paper in an airtight container for up to 1 week.or freeze for up to 1 month. TIP***. for a tidy dividing line between the black and white icing, put a small amount of chocolate fondant in a paper cone or pastry bag fitted with a fine writing tip.Pipe a straight chocolate line across the cookies. Ice one aide up to the line with chocolate and the other side with vanilla.