Prepare your oven and equipment. Preheat oven to 350°F (175°C) and line baking sheets with parchment paper. This prevents sticking and makes cleanup easier.
Combine the dry ingredients. In a medium bowl, whisk together flour, cream of tartar, baking soda, salt, and nutmeg until well incorporated.
Cream the butter and sugar. In a large bowl using an electric mixer, beat butter and 1½ cups sugar on medium-high speed until light and fluffy, about 2-3 minutes. Don’t rush this step – proper creaming creates the perfect cookie texture.
Add wet ingredients to butter mixture. Beat in eggs one at a time, then add vanilla extract, mixing until fully incorporated.
Combine wet and dry ingredients. Gradually add the flour mixture to the wet ingredients, mixing on low speed just until combined. Overmixing will result in tough cookies.
Prepare the cinnamon-sugar coating. In a small bowl, mix together ¼ cup sugar and the ground cinnamon.
Shape the cookies. Scoop dough into 1½-tablespoon sized balls, roll each ball in the cinnamon-sugar mixture, and place 2 inches apart on the prepared baking sheets.
Create thumbprints. Using your thumb or the back of a rounded measuring teaspoon, make an indentation in the center of each cookie, being careful not to press all the way through.
Bake the cookies. Bake for 10-12 minutes until edges are set but centers are still slightly soft. The cookies will continue to firm up as they cool.
Refresh indentations. If the thumbprints have puffed up during baking, gently re-press them while the cookies are still warm.
Cool completely. Allow cookies to cool on the baking sheet for 5 minutes, then transfer to a wire rack to cool completely before filling.
Prepare the eggnog filling. Beat cream cheese and butter until smooth and fluffy. Gradually add powdered sugar, then mix in eggnog, vanilla, nutmeg, and salt until creamy.
Fill the cookies. Transfer the filling to a piping bag (or a zip-top bag with the corner snipped) and pipe into the thumbprint indentations of each cooled cookie.
Add the finishing touch. Lightly dust the filled cookies with additional nutmeg for a festive look and enhanced eggnog flavor.