Combine the coconut milk, sugar, and cinnamon in a blender and blend until smooth.
Chill the coconut milk mixture in refrigerator for 30 minutes.
Make the ice cream following manufacturer's directions for your ice cream maker. Note: I used a Cuisinart and got soft serve consistency ice cream after 20 minutes.
Mix cookie dough chunks in to ice cream. Place ice cream mixture in glass container, and place in freezer until desired consistency is achieved-about 30 minutes.
Notes
The Oatmeal Cookie Dough Bites can be made ahead of time and stored in the refrigerator or freezer.
The Ice Cream mixture can be made ahead of time and stored, well covered, in the refrigerator for up to 3 days.