Melt 1 cup (2 sticks) unsalted butter in a light-colored saucepan over medium heat. Swirl constantly as the butter crackles, foams, and develops amber golden specks with a rich nutty aroma (approx 5 to 6 minutes). Immediately pour into a mixing bowl, scraping all golden flecks from the bottom. Let cool at room temperature for 25 to 30 minutes until soft and creamy (not completely solid).

Add light brown sugar and granulated sugar to the cooled brown butter. Beat with a hand mixer or stand mixer for 2 minutes until creamy and pale. Add the whole egg, extra egg yolk, and vanilla extract. Beat vigorously for 1 minute until fluffy and emulsified.

In a separate bowl, whisk together the flour, cream of tartar, baking soda, fine sea salt, and 1/2 teaspoon cinnamon. Add to the wet ingredients and mix with a rubber spatula just until combined (do not overmix). Cover the bowl and chill in the refrigerator for 45 minutes to firm the butterfat for thick, puffy cookies.

Preheat your oven to 350°F (175°C) and line two large baking sheets with parchment paper. In a small bowl, whisk 1/3 cup granulated sugar and 1.5 tablespoons cinnamon. Scoop rounded 2-tablespoon balls of chilled dough. Roll each ball generously in the cinnamon sugar mixture until heavily coated.

Place dough balls onto prepared baking sheets spaced 2.5 inches apart. Bake at 350°F (175°C) for exactly 9 to 11 minutes until the edges are lightly golden and set, but the centers remain soft and slightly puffy. Do not overbake! Allow cookies to rest on the baking sheet for 5 minutes before transferring to a wire rack.