Preheat oven to 350°F. Line a 9-inch baking pan with aluminum foil.
With a mixer and the paddle attachment, beat the butter on high speed in a large bowl until smooth and creamy, about 1 minute. Add the brown sugar and beat on high speed for 1-2 minutes until creamed. Scrape down the sides and up the bottom of the bowl as needed. With the mixer running on low speed, add the eggs and vanilla extract. Beat on medium-high speed until combined, then beat in the Nutella and kosher salt. Mix until smooth.
With the mixer running on low speed, add the flour, mixing just until combined. Do not overmix.
Pour the batter into the prepared baking pan. Top with sea salt.
Bake for roughly 35 minutes (do the toothpick test to judge doneness).
Allow the brownies to cool completely. Once cool, lift the foil out of the pan using the overhang on the sides. Cut into squares.