Line a baking sheet/pan with parchment paper. Place Nutella in one corner of a plastic bag. Twist so that it does not squeeze out of the top. Cut one corner off at the end of the bag.
Pipe small dollops of Nutella onto the parchment paper, about 1-1 ½ tsp each. You will need about 2 dozen and make some extra just in case. Transfer the baking sheet to the freezer and let sit until firm, about 2 hours.
To Make The Brown Butter
Cut the butter into a few pieces and place in a large skillet or a saucepan over medium heat. Melt the butter completely stirring frequently with the spatula. As the butter heats, it will begin to foam and then bubble. After several minutes, the milk solids will start to become brown on the bottom of the pan (sorry no pics after this - I was a bit pre-occupied). Make sure that milk solids do not stick to the pan. Continue stirring until the butter is evenly browned, being careful not to burn. Remove from the heat and let cool for a few minutes (see the video in the post).
To Make The Cookie Dough
In a medium bowl, whisk together the flour, baking soda and salt.
In the bowl of an electric mixer, combine the sugars and the brown butter. Mix on medium speed until well blended and smooth.
Blend in the egg and egg yolk, vanilla and Greek yogurt, scraping down the bowl as needed.
With the mixer on low speed, blend in the dry ingredients just until incorporated.
Fold in the chocolate chips. Chill the dough in the refrigerator briefly, about 30 minutes.
To Bake Cookies
Preheat the oven to 350ºF (175ºC). For a convection oven, reduce cooking temperature by 25ºF (15ºC). Line baking sheets with parchment paper. We will work in 2-3 batches as the Nutella dollops soften quickly when they are outside of the freezer.
Use a tablespoon, scoop two tablespoons of the cookie dough roll into a ball. Place the cookie dough rolls on the prepared baking sheets, 2-3 inches (5-7.6 cm) apart. Put the remaining cookie dough in the refrigerator.
Take out the frozen Nutella dollops from freezer. Press an indentation into the center of the dough ball to create a bowl shape. Place a dollop of the frozen Nutella in the indentation and pinch together the edges of the cookie dough over the top to completely seal it in the center.
Make a couple of pinches on the top part of the dough so that the finished product will look more appealing. Place the cookies back on the baking sheets, 2-3 inches (5-7.6 cm) apart. By this time Nutella dollops are too soft to pick up with your hand so put them back in the freezer.
Bake the first batch of the cookies at 350ºF (175ºC) until golden brown about 14 minutes, rotating the baking sheet halfway through. After you rotate the baking sheet, start working on the next batch with the remaining dough and nutella dollops as needed.
When the cookies are finished baking, sprinkle lightly with additional sea salt. Let sit a few minutes, then transfer to a wire rack to cool.
You can rewarm the cookie(s) in microwave for a few seconds before you eat.
Once they are completely cool, keep them in an airtight container and store them at room temperature for a week. If you don’t want to bake the whole cookie dough, shape the dough balls and flash freeze on a baking sheet. Then put in a freezer bag and store in the freezer for up to 3 months. When you bake in the future, thaw the cookies while preheating the oven and bake them about 2 minutes longer than the original recipe says.