1. MAKE DOUGH Adjust oven racks to upper-middle and lower-middle positions and heat oven to 400°F Line two baking sheets with parchment paper. Combine flour, cream of tartar, baking soda, and salt in medium bowl. With electric mixer on medium-high speed, beat butter and granulated sugar until light and fluffy, about 2 minutes. Add eggs and rum extract and mix until incorporated. Reduce speed to low, add flour mixture, and mix until just combined.
2. SHAPE COOKIES Roll 1 tablespoon dough into 1-inch ball repeat, placing balls 2 inches apart on prepared baking sheets. Using measuring cup that's been greased on the bottom, press each ball to 1/2-inch round. Bake until edges are lightly browned, 8 to 10 minutes, switching and rotating sheets halfway through baking. Cool 5 minutes on sheets, then transfer to wire rack to cool completely. Repeat with remaining dough.
3. DUST COOKIES Combine confectioners' sugar and nutmeg in small bowl. Using fine-mesh strainer, dust cookies with spiced sugar. (Cookies can be stored in airtight container at room temperature for 3 days.).