Preheat the oven to 350 degrees F. Line 2 baking sheets with parchment paper.
Melt the butter in a medium skillet over medium-high heat. Once the butter begins to bubble it will begin to brown; lower the heat and allow to slowly brown, 3 to 5 minutes. Remove from the heat.
In a stand mixer fitted with the paddle attachment, combine the butter, dark-brown sugar and granulated sugar. Beat until incorporated. (At this point, the butter and sugar will look separated and broken, but that's ok!) Beat in the vanilla, egg, egg yolk and yogurt.
In medium bowl, whisk together the flour, baking soda and salt. Lower the speed on the mixer to low. Gradually add in the dry ingredients, followed by the bittersweet and milk chocolate chips. Mix until everything is fully incorporated.
Begin scooping the dough by tablespoons onto the prepared baking sheets. Once you have 12 tablespoons of dough on each cookie sheet, get the chocolate-hazelnut spread! Make an indentation in each cookie where the chocolate-hazelnut spread will live. Carefully scoop 1 heaping teaspoon of spread into each indentation.
Scoop 1 tablespoon of the remaining cookie dough and place it on top of the chocolate hazelnut spread, creating a dome over the spread. (You want to surround the spread completely with dough so it doesn't ooze out during baking.) Repeat until all cookies are covered. Sprinkle each cookie with sea salt.
You can freeze the cookies for up to a month at this point (freeze them on the baking sheet, and when solid transfer them to zip-close freezer-proof bags), or bake them right away. Bake the cookies until slightly browned on the edges (the tops may be doughy), about 10 to 12 minutes. The cookies may look underdone, but don't worry, they will continue to cook once you remove them from the oven. Cool the cookies on the pan.