Place butter in a medium skillet over medium heat. Melt, then continue to cook, stirring frequently, until the butter foams then begins to brown. Continue cooking until the butter is evenly browned and nutty smelling. Remove from heat and let cool.
While the butter cools, line baking sheets with parchment paper or silicone baking mats. In a medium bowl, whisk together flour, baking soda, and salt.
In a large bowl, combine the sugars. Add in the cooled brown butter, and beat with a mixer until well combined. Beat in eggs, vanilla, and greek yogurt. Add in dry ingredients and mix until just combined. Stir in the chocolate chips. Drop nutella by large spoonfuls into the dough, then stir gently just a little bit to swirl it into the dough. Chill to firm up the dough a bit, about 30-90 minutes or up to overnight.
Preheat the oven to 350 degrees F. Using a medium-large cookie scoop, scoop out cookie dough onto prepared pans. Sprinkle with sea salt.
Bake cookies until cooked and beginning to slightly brown on edges, about 10-12 minutes. Remove from oven, and let cool for a few minutes before transferring to cooling racks.
Notes
Source: adapted from http://www.annies-eats.com/2013/01/11/chocolate-chip-cookies-with-nutella-brown-butter-and-sea-salt/
Recipe by Wright Family Table at https://www.wrightfamilytable.com/nutella-and-brown-butter-chocolate-chip-cookies/