Preheat the oven to 400 degrees F and line several baking sheets with parchment paper. In a large bowl whisk together the flour, cream of tartar, baking soda, and salt. Set aside.
In the bowl of an electric mixer, cream the butter and 1 1/2 cups sugar together until light and fluffy, about 3–5 minutes. Then beat in the eggs and scrape the bowl. Turn mixer on low and slowly add the flour mixture until well combined.
Mix the remaining 1/4 cup sugar and cinnamon together in a small bowl. Use a 1 1/2-tablespoon cookie scoop to measure out dough balls. Roll each ball in your hands to even them out, then roll in cinnamon sugar to thoroughly coat.
Place the balls on prepared baking sheets, 2 1/2 inches apart. Bake for 8–9 minutes, until just barely golden around the edges. Cool for several minutes on the baking sheets before moving.
For the Frosting:
Cream the butter, powdered sugar, vanilla, and cinnamon together until light and fluffy. Scrape the bowl and mix in the marshmallow fluff.
Match up two cookies that are of equal size and shape. Turn the bottom cookies over. Use a piping bag (or zip-bag with the corner cut off) to pipe the filling onto the bottom cookie. Add the top cookie on each sandwich and press down.
NOTE: For thicker fluffier snickerdoodles, chill the dough for one hour before rolling into balls and baking.