01 - Whisk heavy cream, milk, sugar, salt, and peppermint extract until sugar dissolves; add food coloring if desired. Pour mixture into an ice cream maker and churn per manufacturer's instructions. Fold in crushed peppermint candies during the final two minutes. Transfer to container and freeze at least two hours until firm.
02 - Set oven to 350°F (175°C) and line two baking sheets with parchment paper.
03 - Whisk together flour, cocoa powder, baking soda, and salt in a bowl.
04 - Using an electric mixer or whisk, beat butter and sugar until light and fluffy. Add egg and vanilla extract, mixing until combined.
05 - Gradually add dry mixture to wet ingredients, mixing gently until just combined.
06 - Scoop tablespoon-sized dough balls onto baking sheets and flatten slightly. Bake 10 to 12 minutes until set. Allow to cool completely on a wire rack.
07 - Soften ice cream slightly. Place a scoop between two cookies and gently press to form sandwiches. Repeat with remaining portions.
08 - Wrap sandwiches in parchment paper and freeze at least 30 minutes before serving to set.