Assemble the cookies: Line a baking sheet with parchment paper and top with a cooling rack. Place 12 cookies evenly on the tray. Place two tablespoons of mint ice cream on half of the cookies and top with a Thin Mint. Place baking sheet in the freezer for at least an hour up to overnight.
Make the glaze: In a small saucepan, bring cream to a near boil. Place dark chocolate in a medium bowl with coconut oil, and pour warm cream over. Whisk until smooth and shiny.
Remove the sandwiches from the freezer and place on a cooling rack over a clean baking sheet. Pour the glaze over the sandwiches and set in the freezer for 20 minutes. Cookies will keep up to 10 days covered in the freezer.