Add the butter to a light-colored saucepan over medium heat. Light-colored pans allow you to monitor the color change accurately. Swirl the pan constantly as the butter melts, boils, and foams.
Watch for the crackling sound to stop and for small golden-brown specks to form at the bottom of the pan. The butter will smell distinctly nutty.
Immediately pour the brown butter (and all brown specks) into a heat-safe mixing bowl to stop the cooking process. Allow the brown butter to cool until it is lukewarm to the touch (around 15 to 20 minutes).
Mix the Dough
Add the granulated sugar, kosher salt, and vanilla extract to the cooled brown butter. Whisk vigorously until smooth and combined.
Add the room-temperature egg and egg yolk. Whisk until the mixture becomes slightly paler, smooth, and glossy.
Sift the all-purpose flour, baking soda, and cream of tartar into the bowl. Fold gently with a rubber spatula until a cohesive dough forms and no dry flour streaks remain. Do not overmix.
Chill & Shape
Cover the bowl tightly with plastic wrap. Refrigerate the dough for at least 30 minutes to solidify the fats and prevent excess spreading.
In a small bowl, whisk together the granulated sugar and ground cinnamon for the coating.
Use a 1 ½-tablespoon cookie scoop to portion dough into balls. Roll each ball between your palms until smooth, then roll thoroughly in the cinnamon-sugar mixture until fully coated.
Place the coated dough balls onto the prepared baking sheet, leaving 2 inches of space between each cookie.
Bake & Scoot
Bake for 11 to 12 minutes, until the edges are set and golden brown, but the centers still look soft and slightly underbaked.
The Cookie Scoot: Immediately upon pulling the tray from the oven, place a large round cookie cutter over a hot cookie and gently swirl it in a circular motion against the baking sheet for 3–5 seconds. This pulls in stray edges and creates a perfectly round, thick cookie.
Allow the cookies to cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely.
Notes
Chill the Dough: Do not skip the 30-minute minimum chill. It solidifies the brown butter fat to prevent the cookies from spreading too flat in the oven.
Cool the Brown Butter: Let the browned butter cool to lukewarm before adding the sugar and eggs. Hot butter will scramble the eggs and dissolve the sugar prematurely.
Don't Omit Cream of Tartar: Cream of tartar is essential for authentic snickerdoodles; it provides the signature tangy flavor and reacts with baking soda to create a soft, chewy texture.
The Cookie Scoot: Reshape the cookies immediately upon removing them from the oven by swirling a round cookie cutter around each hot cookie to pull in the edges.
Maintaining Softness: Store baked cookies in an airtight container with a slice of white bread to keep them soft and chewy for up to 4 days.