Preheat oven to 375°F (190°C) and line a baking sheet with parchment paper.
Combine 3 tablespoons sugar and cinnamon in a small bowl. Set aside.
Whisk flour, cream of tartar, baking soda, salt, and nutmeg together in a separate bowl.
Beat softened butter and ¾ cup sugar for approximately 2 minutes until light and fluffy.
Beat in the egg yolk.
Add eggnog and vanilla and mix until combined.
Gradually add the dry ingredients and mix just until a soft dough forms.
Scoop approximately 1½ tablespoons of dough per cookie.
Gently roll each portion into a ball.
Roll each dough ball generously in cinnamon sugar.
Arrange approximately 2 inches apart on the prepared baking sheet.
Bake for 8–10 minutes, until the edges are set but the centers remain soft.
Cool on the baking sheet for 5 minutes.
Transfer to a wire rack and finish cooling.