In a medium bowl, whisk together the flour, cream of tartar, baking soda, salt and nutmeg. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment, cream together the butter and sugar on medium-high until light and fluffy, about 3 to 4 minutes. One at a time, add the egg and egg yolks, mixing well after each addition. Mix in the rum extract. Scrape down the bottom and sides of the bowl as needed.
Add the flour mixture and beat on low speed until combined.
Chill the dough for 30 minutes. Preheat oven to 350℉. Line baking sheets with parchment paper.
Prepare the nutmeg-sugar mixture by whisking together ¼ cup sugar and 2 teaspoons ground nutmeg in a small bowl (and cinnamon if using). Use a medium cookie scoop to scoop dough and roll into balls. Roll each dough ball in the nutmeg-sugar and place on prepared baking sheet about 2 inches apart.
Bake 10 to 12 minutes until edges are set and the centers are puffy. Cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely.
Notes
Rum extract is easy to find in your local grocery store during the holidays. You can use rum, but it won't have as much flavor.Cream of tartar provides a tangy flavor and chewy texture snickerdoodles are known for. You can find it in the spice aisle or baking aisle at your local grocery store.Store cookies in an airtight container at room temperature for up to 5 days.Freeze for up to 3 months. Form dough into a log and wrap in plastic wrap. Defrost in the refrigerator before scooping into balls and baking. You can also freeze baked cookies for up to 3 months. Wrap in plastic wrap to prevent freezer burn.