How to Make It
Prepare the Cake Layers: Preheat oven to 350°F. Process flour, crystallized ginger, baking powder, baking soda, salt, cinnamon, ground ginger, and nutmeg in a food processor until crystallized ginger is finely ground, about 1 minute. Set aside.
Beat salted butter with a heavy-duty electric stand mixer on medium speed until creamy. Gradually add light brown sugar, beating until light and fluffy. Add egg yolks, 1 at a time, beating just until blended after each addition. Stir together coffee and molasses in a glass measuring cup. Add flour mixture to butter mixture alternately with coffee mixture, beginning and ending with flour mixture, beating on low speed just until blended after each addition.
Place egg whites in a bowl. Beat with an electric mixer on high speed until stiff peaks form. Gently fold egg whites, in thirds, into batter, folding just until incorporated after each addition.
Spoon batter into 3 greased (with vegetable shortening) and floured 9-inch round cake pans. Bake in preheated oven until a wooden pick inserted in center of cakes comes out clean, 19 to 22 minutes.
Meanwhile, prepare the Espresso Simple Syrup: Bring coffee and granulated sugar to a boil in a small saucepan over medium-high. Boil, stirring occasionally, until reduced to about 1⁄2 cup, 5 to 6 minutes.
Remove cakes from oven, and cool in pans on wire racks 10 minutes. Transfer from pans to wire racks; brush evenly with warm Espresso Simple Syrup. Cool completely, about 1 hour.
Prepare the Vanilla Whipped Cream Frosting: While Cake Layers cool, beat cream and vanilla bean paste with an electric mixer on medium speed until foamy, 1 to 2 minutes. Gradually add granulated sugar, beating until stiff peaks form, about 2 minutes. (Do not overbeat.)
Assemble the cake: Spread frosting between layers and on top and sides of cake. Gently press crushed ginger cookies around the bottom of the cake to make a 1 1/2-inch band.