These cookies are sure to please everyone in the house.
Preheat oven to 350 degrees. In a medium bowl, whisk together flour, cream of tartar, baking soda, and salt; set aside. With an electric mixer, cream butter and 1 2/3 cups sugar until light, scraping down sides of bowl as needed. Add egg and vanilla; beat until combined. Add flour mixture; beat, scraping bowl as needed, until dough comes together when squeezed (it will appear dry).
Make the topping: In a small bowl, mix together remaining 1/4 cup sugar and cinnamon.
Shape dough. Scoop 48 level tablespoons. Squeeze each tightly with fist; roll into balls. Roll balls in topping to coat evenly. Place 1 1/2 inches apart on baking sheets; flatten with bottom of a glass. Sprinkle tops with remaining topping (there may be excess).
Bake, one sheet at a time, until tops are puffed and crackly, and bottoms are golden brown, 10 to 12 minutes. Cool slightly on sheets; transfer to a rack to cool completely.
These cookies will keep for up to three days in an airtight container at room temperature; include a few marshmallows to help the cookies stay moist.