In a large mixing bowl, combine the softened butter, light brown sugar, and granulated sugar. Beat until light and fluffy.

Add the egg and vanilla extract, mixing until fully incorporated.

In a separate bowl, whisk together the flour, kosher salt, baking soda, and cream of tartar. Gradually add the dry ingredients to the wet mixture, stirring until a smooth dough forms.

Wrap the dough in plastic wrap and refrigerate for at least 1 hour.

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

Scoop out tablespoons of dough and roll them into balls. Roll each ball in the cinnamon-sugar mixture until evenly coated.

Arrange the coated dough balls on the prepared baking sheets, spacing them about 2 inches apart. Bake for 8–10 minutes, or until the edges are set but the centers remain soft.

Transfer the cookies to a wire rack and let them cool completely before adding the ganache.

In a small saucepan, gently heat the eggnog until warm but not boiling.

Place the chopped white chocolate in a heatproof bowl. Pour the warm eggnog over the chocolate and let it sit for a minute.

Stir the mixture until smooth and creamy, then mix in the rum (or rum extract) and freshly grated nutmeg. Let the ganache cool slightly to thicken.

Flip half of the cookies upside down. Pipe or spoon a dollop of eggnog ganache onto the flat side of each cookie.

Place another cookie on top, gently pressing to spread the ganache evenly.

Allow the ganache to set for 10–15 minutes before serving.