Place a large mixing bowl into the freezer for 10-15 minutes to chill.
After the bowl has chilled, remove the canned coconut milk from the fridge (do not shake it). Scoop out the coconut cream and place it in the bowl, leaving behind the liquid.
Whip the coconut cream until stiff peaks form and the consistency is similar to that of whipped cream.
Add in the cocoa powder, powdered sugar, and collagen*, scraping down the sides of the bowl frequently.
Add vanilla extract, vodka*, and milk then mix until combined.
Fold in half of the sugar cookie dough and place the mixture into an ice cream container or other airtight container. Sprinkle remaining cookie dough on top.
Freeze for 7-8 hours or overnight. When ready to serve, allow the ice cream to thaw for 15-20 minutes.