In a heavy-bottomed sauce pan, place the butter. Cook the butter over medium-low heat until frothy. Once melted and frothy, keep an eye on the butter. Cook until it turns a light brown and smells nutty. It will take awhile, about 10 minutes or so.
One the butter is warmed, remove it from the pan. Place it into a shallow container, and place in the refrigerator until cool.
In a large bowl, whisk the flour, baking soda and salt. Set aside.
In the bowl of a mixer fitted with a paddle attachment, mix the brown butter and both sugars. Beat until combined.
Add the egg, egg yolk, vanilla. Beat until combined.
With the mixer on low, slowly add the dry ingredients. Mix until just combined.
Using a spatula, mix in the chocolate chips.
Refrigerate the dough for at least 2 hours or overnight.
Place the jar of Nutella in the fridge for at least two hours in order for it to be stiff enough to stuff the cookies.
Preheat the oven to 350 degrees F
Line baking sheets with parchment paper or silicon baking mats.
Roll about 1 teaspoons worth of dough into a ball and flatten like a pancake.
Place a scant teaspoon of Nutella in the center of the disk.
Take another teaspoonful of dough and flatten into a disk, Place the second piece of dough over the Nutella, and seal the edges. Make sure that all the seams are completely sealed.
Place the cookies about 2 inches apart on the prepared pans.
Bake for 9 to 11 minutes.
Allow the baked cookies to cool on the cookie sheet for about 5 minutes, then transfer them to a cooling rack to cool completely.