Add eggnog and protein powder to a large bowl and mix with a hand mixer until smooth and thick.  Add condensed milk, bourbon, and spices and continue to mix until well combined.

Pour the ice cream base into a 1.5 liter loaf pan or similar freezer-safe container.  Freeze for about 2-3 hours - the ice cream should be firm but still able to be stirred with effort.

Pour gingersnap syrup and crumbled gingersnap cookies on top of ice cream.  Using a spoon or knife, swirl the syrup and cookies throughout the ice cream base, being careful not to overmix (you want to still be able to see the definition of the gingersnap swirls).  Return to freezer for 1-2 hours longer before serving.