1. In a mixing bowl, whisk together heavy cream, whole milk, sugar, and peppermint extract until sugar is dissolved.
2. Pour the mixture into an ice cream maker and churn according to the manufacturer's instructions. Fold in mini chocolate chips.
3. Transfer the ice cream to a container and freeze for at least 2 hours.
4. Preheat the oven to 350°F (175°C). Line a baking sheet with parchment paper.
5. In another bowl, mix gluten-free flour, cocoa powder, baking soda, and salt.
6. In a separate bowl, beat together softened butter, brown sugar, and white sugar until creamy. Add eggs and vanilla extract, and mix well.
7. Gradually add the dry ingredients to the wet ingredients and mix until combined.
8. Scoop dough onto the prepared baking sheet and flatten slightly. Bake for 10-12 minutes. Let cool completely.
9. To assemble, place a scoop of ice cream between two cookies and press gently. Freeze for another hour before serving.