Preheat oven to 350°F. Line sheet pan with parchment paper.
In bowl of stand mixer fitted with paddle attachment, or in large bowl with hand-held mixer, beat butter and sugar together on high speed until pale and creamy. Add eggs one at a time, mixing after each, followed by the vanilla.
In separate bowl, combine flour, cocoa powder, baking soda and salt. Add to butter mixture all at once and mix until incorporated.
Shape into rounded tablespoons and place on prepared sheet pan. Bake until surface is cracked and edges are dry, about 10 minutes. Let cool completely.
To prepare frosting, in bowl of electric mixer, beat powdered sugar, butter, salt, heavy cream, and peppermint extract on low speed until it comes together. Increase speed to high and beat for 2-3 minutes until light and creamy.
Use clean paintbrush to paint red gel food coloring up the interior sides of large piping bag fitted with a star tip, making 4 lines total. Fill bag with frosting. Pipe frosting onto bottom of 1 cooled chocolate cookie and place another chocolate cookie on top. Repeat with remaining cookies.Store cookies in airtight container at room temperature for up to 5 days