Line a 10-inch (or 9-inch) cake pan or springform pan with plastic wrap and set aside.
In a large, chilled bowl, whip heavy cream to soft peaks. Add the ground ginger and whip to stiff peaks.
Using a rubber spatula, gently fold in the sweetened condensed milk into the whipped cream. Fold in chopped candied ginger.
Pour ice cream into the plastic lined cake pan, cover with more plastic wrap and freeze for 6 hours or overnight.
Preheat oven to 350 degrees. Place parchment paper in the bottom of two 10-inch (or 9-inch) cake pans or springform pans. Grease the sides.
In a medium bowl, whisk together the flour, baking soda, cinnamon, salt, nutmeg, and allspice. Set aside.
In a large bowl, beat butter and sugar together until creamy, about 3-4 minutes. Mix in pumpkin, egg and vanilla extract. Add flour mixture until combined. Fold in chopped chocolate.
Divide and spread the cookie dough out evenly into the pans. Bake for 20-22 minutes or until set.
Remove from oven and let cool for about 15 minutes, then transfer to cooling rack to cool completely.
Once completely cooled, arrange one layer of the cookie cake on a large plate or platter. Remove ice cream from freezer, unwrap, and place on top. Sandwich with the second layer of the cookie cake. Slice and serve immediately. Store any leftovers in the freezer covered in foil or plastic wrap.