Preheat oven to 325°F. Line 2 baking sheets with parchment paper (or a silpat silicone baking mat). Set aside.
In a large mixing bowl, stir together the shredded coconut, sweetened condensed milk, and vanilla extract until well combined. Set aside.
In the bowl of a stand mixer, or a medium mixing bowl with a hand mixer, beat together egg whites and salt until stiff peaks form.
Gently fold the whipped egg whites into the coconut mixture with a rubber scraper.
Use a medium cookie scoop to portion out the coconut macaroon mixture onto the prepared baking sheets. Gently shape each portion into a nest by pressing down the center of each scoop with your thumbs (or the back of a tablespoon measure). Press the edges in with your other hand as needed to keep a nice shape.
Bake for 20-25 minutes, rotating the pans halfway through baking, until the tops and edges are golden brown.
Remove from the oven and press down the center of the nests again. Allow to cool on the pans for 5-10 minutes to allow them to set. Then move to a wire cooling rack to cool completely.
When cooled, place 1-2 tablespoons of Nutella into the center of each next. Place 3 egg-shaped candies into each next.