In a medium bowl, thoroughly stir together the 3 cups flour, baking soda, cinnamon, ginger and salt; set aside. In a large bowl, with an electric mixer on medium speed, beat together the butter, shortening, and brown sugar until light and well blended. Beat in the egg yolk until evenly incorporated and fluffy. Beat in molasses. Stir or beat in the flour mixture until evenly incorporated. If the dough seems very soft, stir in up to 3 tbls more flour. Divide the dough in half. Place each portion between large sheets of wax paper. Roll out each portion 1/4" thick; check underside of the dough and smooth out any wrinkles that may form. Stack the rolled portions (paper still attached) on a baking sheet. Refrigerate for 1 1/2 hours, or until chilled and firm or freeze for 45 minutes to speed chilling. (the dough may be held for up to 8 hours). Preheat the oven to 325*.Grease several baking sheets or coat with nonstick spray.
In a medium bowl, with an electric mixer on low speed (use a whisk-shaped beater, if available), beat the powdered sugar and egg white until blended.Increase the speed to high and beat until glossy and stiffened. Beat in lemon juice. If necessary thin the mixture with water to produce a smooth spreadable glaze. Cover the bowl with a damp kitchen cloth to keep glaze from drying out; set aside.
Working with one portion at a time, leaving remainder chilled.gently peel away and then pat into place one sheet of wax paper.Flip over and peel away and discard second sheet of wax paper.Using a 2 1/2"-3" round or fluted cookie cutter, cut out enough cookies to fill one sheet.2" apart.(if at any time,dough gets too soft to work with easily, return dough to refrigerator or freezer to re-chill. Check the consistency of the glaze and thin it with a few drops of water, if necessary. Using a table knife, spread a smooth, even layer of glaze over the top of each cookie, spreading it all the way to the edges. Bake the cookies as soon as the glaze is on. Reroll any dough scraps and continue baking as directed above. Bake the cookies, one sheet at a time, in the middle of the oven for 11-13 minutes or until glaze is just tinged with brown. Reverse sheet halfway through baking to ensure even browning from front to back. Transfer the sheet to wire rack and let stand until the cookies firm up slightly. 1-2 minutes. Using a spatula, transfer the cookies to wire rack to cool completely. Store in a single layer or layered with wax paper in an airtight container for up to 2 weeks or freeze up to 1 month.