Brown butter in a medium saucepan (for a step by step guide of browning butter, see the directions of this recipe here). Pour browned butter, using a rubber spatula to scrape out any excess, into the bowl of an electric stand mixer and allow to cool until lukewarm, about 20 - 30 minutes.
In a mixing bowl, whisk together flour, baking soda and 1/4 tsp kosher salt, set aside. Add light-brown sugar to cooled butter in stand mixer fit with paddle attachment. With mixer set on medium-low speed, blend mixture together until well combine, about 1 minute. Add in vanilla bean seeds, and vanilla then add in eggs one at a time and mix until well combine after each addition.
Set mixer on low speed and slowly add in dry ingredients and mix just until combine. Mix in chocolate chips (if you want some chocolate chips showing through as those pictured, I like to set some of the chocolate chips aside then I gently press about 5 of them into the top of each cookie dough ball after shaping). Transfer dough to an airtight container and chill in refrigerator about 1 1/2 hours.
Preheat oven to 350 degrees. Remove dough from refrigerator and scoop dough out about 2 1/2 Tbsp at a time and shape into balls, then align them on a large sheet of parchment or wax paper.
Evenly flatten dough balls until you have about a 3 1/4-inch circle, then place 1 tsp chilled Nutella in the center on top of each. Carefully fold dough up and around Nutella, covering it entirely (if you find it beginning to seep through in some areas, I just added a chocolate chip to that spot to act as a plug).
Transfer to a Silpat lined cookie sheet (you can fit 8 cookies per sheet) and bake in preheated oven 10 - 12 minutes until golden brown. Remove from oven and immediately sprinkle cookies with coarse sea salt (you can also sprinkle them with sea salt before baking as the salt sticks better that way, I actually did a tiny before and after). Allow to cool several minutes on cookie sheet before transferring to a wire rack to cool. Store in an airtight container.