PREHEAT the oven to 400°F (225°C).
SIFT several cups of flour back and forth between 2 large bowls 3 to 4 times.
WEIGH 396 grams of the sifted flour on a digital kitchen scale and place it in a bowl. If you don't have a scale, use 3 cups + 1 tablespoon of sifted flour. (Measure carefully. Spoon the sifted flour into the measuring cup and scrape the cup flat with the straight edge of a knife.)
WHISK the cream of tartar, baking soda, and salt into the flour.
CREAM the butter and 1⅔ cups (330 grams) of sugar in a separate bowl with an electric mixer on high for 1½ to 3 minutes, or until the texture progresses from sandy to creamy. Please note: The butter should be between 62 to 65°F (16 to 20°C). Colder butter could prevent the cookie from spreading enough as it cooks. Warmer butter will cause the cookie to spread too much when baking and may create a more crispy cookie. If the butter gets too warm, refrigerate it for a few minutes before creaming it. BLEND the vanilla and eggs (one at a time) into the creamed sugar and mix on medium speed for 30 seconds. Please note: Take the eggs straight from the refrigerator before blending. They should be cold. MIX the flour mixture into the wet ingredients. Use an electric mixer on low and mix until the flour is incorporated. Scrape the sides of the mixing bowl with a rubber spatula and blend again.
STIR the cinnamon with 3 tablespoons (38 grams) of sugar in a small, shallow bowl until well blended.
SCOOP the cookie dough with a 2-tablespoon cookie scoop.
ROLL the cookie dough ball in your palms until smooth. Then roll the ball in the cinnamon-sugar mixture until completely coated.
PLACE the cookie dough ball on a heavy duty aluminum cookie sheet lined with parchment paper (or a silicone mat).
REPEAT rolling the cookie dough balls and place them all on the baking sheet 2 to 3 inches apart.
BAKE for 8 to 10 minutes until the edges are set, but the middle does not look completely solid. Use your judgment here. The cookie should not be doughy. Cook until the cookies look almost done.
REMOVE the baking sheet from the oven and turn the oven off. Cool the cookies for 1 minute.
SHAPE the cookies with a cookie ring. Circle the cookie with a cookie ring larger than the cookie. Using a circular motion, swirl the cookie ring around the cookie. This will pull in the snickerdoodle sides, creating a round, uniform shape. Repeat with the remaining cookies.
PLACE the cookie sheet on the cooling rack for 5 minutes.
TRANSFER the cookies from the baking sheet to the cooling rack and allow them to cool completely, about 45 minutes to 1 hour.
REST the cookies. Place the cooled cookies in an airtight container for a minimum of 1 hour, but 2 to 3 hours is better. (A better option is to freeze them overnight. See instructions below.)
SERVE with hot chocolate or a glass of cold milk.