Preheat your oven to 350°F (180°C) and line three sheet pans with parchment paper.

In a medium bowl, whisk together the all-purpose flour, baking soda, fine salt, and cream of tartar.

In a stand mixer, beat the unsalted butter until creamy, then add granulated sugar and mix until fluffy.

Incorporate the egg, cocoa powder, red food coloring, and vanilla extract into the mixer and combine until smooth.

Gradually mix in the dry ingredients until just combined, avoiding over-mixing.

Using a cookie scoop, portion out 3 oz balls of dough and place them on the prepared sheet pans.

Bake for 13-16 minutes, banging the pans against the oven rack every few minutes.

Allow cookies to cool on the sheet pans for about 10 minutes, then transfer them to a wire rack.

In a small saucepan, melt butter and whisk in cream cheese, vanilla, and salt, then add confectioners' sugar until smooth.

Dip half of each cookie in the icing and sprinkle with holly sprinkles, allowing them to set before serving.