• Adjust an oven rack to the middle of the oven. Preheat the oven to 350F [180C]. Line three sheet pans with aluminum foil or parchment paper (see note).
• In a small bowl, whisk together the flour, baking soda, salt, and cream of tartar.
• In the bowl of a stand mixer fitted with a paddle, beat the butter on medium speed until creamy, about 1 minute. Add the granulated sugar and beat on medium speed until light and fluffy, 2 to 3 minutes. Add the egg and mix on low speed to combine. Add the cocoa powder, red food coloring, and vanilla, and mix again on low until combined. Use a spatula to scrape down the sides as needed and completely combine the food coloring into the batter. Add the flour mixture and mix on low speed until completely combined.
• Form the dough into 3 oz [85 g] balls [1/4 cup]. Place 4 cookies an equal distance apart on the sheet pans. Bake the cookies one pan at a time. Bake until the dough balls have spread out but are puffed slightly in the center, 8 minutes. Lift one side of the sheet pan up about 4 in [10 cm] and gently let it drop down against the oven rack, so the edges of the cookies set and the center falls back down. After the cookies puff up again in 2 minutes, repeat lifting and dropping the pan. Repeat a few more times to create ridges around the edge of the cookie. Bake for 13 to 16 minutes total, until the cookies have spread out and the edges are set and golden but the centers are not fully cooked.
• Transfer the pan to a wire rack. Let the cookies cool for 10 minutes, then move them to a wire rack to cool completely before icing them.

For the icing

• Melt the butter in a medium bowl. Add the cream cheese, 2 tablespoons of water, vanilla, and salt, and whisk to combine. Add 1 cup [120 g] of the confectioners' sugar and mix with a spatula to combine. Add more sugar as needed, until the desire consistency is reached. You want the icing to be thick but not too thick - it should be thin enough to cling to the surface when you dip the cookie into it. If your icing is too thick, you can add more water as needed to thin it out.
• To assemble: dip half of a cooled cookie into the icing. Decorate with holly sprinkles or other decoration if desired. Let the icing set before serving.