Preheat the oven to 350° and prepare a cookie sheet with parchment paper.
In a medium saucepan, cook butter over medium heat while whisking constantly. The butter will begin to foam, and start to turn brown at the bottom of the pan.
Once the butter begins to brown, transfer immediately to a separate bowl. Let cool for 15 minutes.
In a stand mixer fitted with a paddle attachment mix browned butter and sugars. Mix until combined.
Add egg, egg yolks, greek yogurt and vanilla extract.
Add dry ingredients and mix until just combined.
Let the dough sit for 5 - 10 minutes to allow the dough set up and become more firm.
Take about two tablespoons of dough and roll it into a ball.
Roll the ball in the brown sugar.
Place on a cookie sheet, about 2 inch apart from each other and bake for 8-11 minutes, or until the edges of the cookies begin to turn golden brown.
Allow cookies to cool on the baking sheet.