In a small saucepan over medium heat, melt the butter for roughly 5 minutes, swirling the pan every 20 seconds or so. Heat until the white milk solids become a medium brown color. Remove from heat and allow to cool slightly.
In a large bowl, combine browned butter, granulated sugar, and brown sugar. Whisk to combine. Add in egg and yolk, whisking until the mixture turns slightly lighter in color.
Sprinkle in salt, baking soda, cream of tartar, yogurt/sour cream, vanilla, and flour. Fold batter together using a spatula. Mixture will be relatively wet.
Combine sugar and cinnamon in a small bowl. Roll 2-3 tablespoons of batter into a ball, then dip completely in cinnamon sugar. Place on prepared baking sheet, leaving at least 1.5 inches between each cookie. Repeat with remaining cookies.
Bake for 12-14 minutes, until the cookies have started to wrinkle but are still pale in color (NOT golden brown!). Remove from oven and let sit on baking sheet for 10 minutes (they will continue to cook as they cool).
While the cookies are baking, make the frosting. Combine butter, dark brown sugar, and powdered sugar in a standing mixer. Whisk on medium speed until batter becomes light and fluffy, about 1 minute.
Once cookies have cooled completely, top with frosting. Or don’t, because to be honest these cookies are AMAZING on their own, too!!