Preheat the oven to 350°F. Line an 8"x8" pan with parchment paper. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment, (or using hand beaters), cream the butter and sugar on medium-high speed until smooth and creamy, about 2 minutes. Using a rubber spatula, scrape down the sides of the bowl.
Add the eggs and vanilla extract. Beat until combined.
Add in 1 cup of Nutella, and the salt. Mix until smooth and fluffy. Scrape down the sides of the bowl as needed.
Add the flour. Mix until just combined. Do not overmix. Using a rubber spatula, fold in the chocolate chips.
Pour the batter into the prepared baking pan. Drop teaspoonfuls of the remaining 1/3 cup of Nutella along the top. Using a knife, swirl the Nutella into the batter. Top with a sprinkle of flaky sea salt.
Bake the Nutella Brownies for 32-35 minutes. Be careful not to over bake! Keep your eye on them. Test the brownies by using a toothpick to determine doneness. You want the brownies to come out with a couple of moist crumbs on the toothpick.
Remove from the oven and set on a wire rack to cool. When cool, carefully lift the parchment paper (or aluminum foil) out of the pan, and cut into squares. You can store these in an airtight container for up to 3 days.