Preheat oven to 350 degrees. Line a baking sheet with parchment paper or silicone baking mats, set aside.

In a large saucepan over low heat, melt butter. Add brown sugar and stir with a heatproof spatula. Remove mixture from heat. Add in water, then chocolate chips, stir until chips are melted.

Beat in eggs one at a time, then add the vanilla. Fold flour, baking soda, and salt. Mix until a buttery dough forms (it will be greasy looking).

Roll dough into 1½” balls and place on a baking sheet. Place into oven and bake for 8-10 minutes. Remove from oven and allow to cool on baking sheet for 3-4 minutes before transferring to a wire rack to cool completely. 

While the cookies are cooling, in the bowl of a stand mixer or a large mixing bowl with a hand mixer, cream butter and salt for 1 minute. Turn mixing speed to low, gradually add the powdered sugar one cup at a time. Add the milk and peppermint extract (and food coloring or candy canes if desired). Gradually turn speed up and continue beating for 2 minutes until light and fluffy. 

Place filling into a large piping bag fitted with a large round tip, and pipe onto one side of a cooled cookie. Place a “top” on it (you will want to try to match up similar size/shape ones). Allow cookies to sit for 30 minutes before serving.