Prepare the Cookie Dough:

• 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.

Roll and Bake the Cookies:

• 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.

Make the Eggnog Ganache Filling:

• 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.

Assemble the Cookies:

• 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.