2) Roll out doughs separately to approximately 0.5-cm thickness. Place peppermint dough on top of chocolate and press together around the edges. Using waxed paper or flexible cutting board underneath, roll dough into log. Wrap in wax paper and refrigerate for 2 hours.
3) Preheat oven to 190C/Gas 5.
4) Remove dough from the refrigerator and cut into 1/-cm slices.
5) Place cookies 2-cm apart on greased baking sheet, parchment, or silicone baking mat and bake for 12 to 13 minutes, rotating the pan halfway through cooking time. Remove from oven and let sit on baking sheet for 2 minutes, then move to a wire rack to cool completely. Store in an airtight container for up to 1 week.
For the sugar cookies dough:
1) Sift together flour, baking powder, and salt. Set aside. Place butter and sugar in large bowl of electric stand mixer and beat until light in color. Add egg and milk and beat to combine.
2) Put mixer on low speed, gradually add flour, and beat until mixture pulls away from the side of the bowl. Divide the dough in half, wrap in waxed paper, and refrigerate for later use.