Prepare the coffee mixture by combining cooled brewed coffee, vanilla extract, ground ginger, ground cinnamon, and ground nutmeg in a shallow dish. Stir well and set aside.

In a large mixing bowl, whip the heavy cream until soft peaks form. Gradually add powdered sugar and continue whipping until stiff peaks form. Gently fold in the mascarpone cheese until smooth.

Dip each gingerbread cookie quickly into the coffee mixture and layer half of them in a 9x9-inch dish. Spread half of the mascarpone mixture over the cookies. Repeat with remaining cookies and mascarpone mixture, finishing with a layer of mascarpone on top.

Cover the dish with plastic wrap and refrigerate for at least 4 hours or overnight. Dust with cocoa powder and sprinkle crushed gingerbread cookies before serving.