In a large bowl, cream the softened butter and 1 1/2 cups sugar until light and fluffy, about 2 minutes. Beat in the eggs, eggnog, and vanilla.

In a separate bowl, whisk together the flour, cream of tartar, baking soda, salt, and 1/2 tsp nutmeg. Stir into the wet mixture until a soft dough forms. Chill 1 hour.

Preheat oven to 350°F. Line two baking sheets with parchment paper.

Stir together the 1/3 cup sugar, cinnamon, and remaining 1/2 tsp nutmeg in a small bowl. Roll the dough into 1 1/2-inch balls and roll each in the cinnamon-sugar mixture.

Place 2 inches apart on the prepared sheets. Bake 10–12 minutes, until the edges are set and the centers look just slightly underdone. Cool on the trays 5 minutes, then on a wire rack.