Grease the bottom and sides of an 8- by 8-inch baking pan with butter. Line the pan with parchment paper, leaving a 2-inch overlap on the sides.
In a medium glass or stainless steel bowl, stir together sweetened condensed milk, vanilla, bittersweet chocolate chips, Nutella, and butter.
Form a double-boiler by setting the bowl on a medium pot of gently simmering water. The water level should be low enough that the bottom of the bowl does not touch the water. Stir until the chocolate chips are melted and the mixture is smooth, 5 to 7 minutes.
Scrape the mixture into the prepared pan, spread the top smooth with a spatula, and sprinkle with sea salt. Refrigerate until the fudge is firm, at least 2 hours.
Run a knife under hot water, dry it off, and run it around the edges of the pan to loosen the fudge. Using the overhanging parchment paper, lift the fudge out. Peel off the parchment paper. Cut the fudge into 3/4-inch squares. Store in the refrigerator in an airtight container or wrapped well in plastic wrap and foil.