Preheat the oven to 350℉.
First, prepare your brown butter: In a small saucepan, add in 8 Tbsp (1 stick) unsalted butter over medium-low heat and allow the butter to melt. Once it has melted, do not stray far from the stove as the browning process happens quickly! The melted butter will bubble, pop and sizzle violently; this is normal. After about 5 or so minutes, it may become foamy. Swirl the pan occasionally to discourage burning. You'll begin to notice some browned bits on the bottom of the pan; continue swirling the pan and remove from the heat when the butter is amber in color and smells nutty.
Pour the brown butter into the bowl of a stand mixer with the remaining 4 Tbsp softened butter. Allow to sit for 5 minutes to help further soften the remaining butter. Then, add in the sugars and beat with the paddle attachment until combined, about 1 minute. Add in the egg, followed by the egg yolk, mixing well, followed by the vanilla. Lastly, add in your baking soda, cream of tarter, salt, and flour and mix until just combined; set aside. Meanwhile, in a small bowl, mix together the remaining granulated sugar and cinnamon.
Line two baking sheets with parchment paper. Using a Tablespoon-size cookie dough scoop, portion out dough balls one at a time. Drop a rounded dough ball into the cinnamon sugar mixture and toss gently to coat. Place the dough balls 2" apart on the baking sheets.
Bake for 10-12 minutes, rotating the pans halfway through baking time to ensure even baking. Remove from the oven and allow to cool on the baking sheets for 5 minutes before carefully transferring to a wire rack to cool completely. Cookies may appear puffy and deflate; this is normal as they are a crisper cookie than a traditional puffy one. If you have any leftover cinnamon sugar, sprinkle it over the still-warm cookies.