Cream the unsalted butter and both sugars until light and fluffy, about 3-5 minutes. Then mix in the medium egg and vanilla extract until well combined.
Sift together the all-purpose flour, baking soda, cream of tartar, and kosher salt. Blend this mixture into the wet ingredients until just combined to form a thick dough.
Scoop tablespoon-sized dough balls and roll them in cinnamon sugar to coat. Place on a parchment-lined baking sheet and use your thumb or a teaspoon to create a thumbprint in the center.
Preheat your oven to 350°F (175°C) and bake the cookies for about 7 minutes, or until they are just set. Gently press down on the thumbprint if needed.
In a microwave-safe bowl or double boiler, melt the white chocolate with the eggnog until smooth. Stir in the optional rum and grated nutmeg if using, for extra festive flavor.
Once the cookies have cooled completely, use a teaspoon to fill each thumbprint with the creamy ganache. Allow to set at room temperature or refrigerate until firm.
Notes
Optional: Sprinkle with additional grated nutmeg before serving for an extra touch of holiday spirit!