Add coconut milk to a heavy-bottomed sauce pan and bring to a low boil over medium heat. Lower heat to medium-low and whisk in Monkfruit sweetener, stevia powder, and xanthan gum until dissolved.
Simmer mixture until reduced by half (about 1 hour), whisking frequently to prevent burning. Remove from heat and set aside to cool.
Whisk in casein protein powder until no lumps remain (strain if needed). Add more casein protein powder 1 tbsp at a time if needed to reach the consistency of sweetened condensed milk. Set aside.
Add eggnog and protein powder to a large bowl and mix with a hand mixer until smooth and thick. Add condensed milk alternative, 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.