Preheat your oven to 350°F (175°C). Line baking sheets with parchment paper.

In a medium bowl, whisk together the flour, baking soda, cream of tartar, salt, cinnamon, and nutmeg. Set aside.

In a large bowl, beat the softened butter and granulated sugar until light and fluffy, about 2-3 minutes.

Add the eggs, vanilla extract, and eggnog to the butter mixture. Beat until well combined.

Gradually add the dry ingredient mixture to the wet ingredients, mixing until just combined.

Scoop out tablespoon-sized amounts of dough and roll them into balls. Place them on the prepared baking sheets, spaced about 2 inches apart.

Gently press your thumb (or the back of a spoon) into the center of each cookie to create a small indentation.

Bake in the preheated oven for 10-12 minutes or until the edges are lightly golden. The centers may look slightly underbaked; this is normal.

Remove from the oven and let the cookies cool on the baking sheets for about 5 minutes before transferring them to wire racks to cool completely.

In a small bowl, mix together the powdered sugar, softened butter, eggnog, and vanilla extract until smooth and creamy.

Once the cookies are completely cooled, fill each thumbprint with a dollop of the eggnog frosting.

Optionally, sprinkle a pinch of ground nutmeg over the frosting for an extra festive touch.