In the bowl of a stand mixer fitted with the paddle attachment, add the butter and sugar and mix on medium speed for 2 minutes, until light and fluffy.
Add the eggs and vanilla and mix again until well combined. Scrape down the sides of the bowl if necessary.
Turn the mixer on low speed and carefully add the flour and salt. Mix until well combined on low speed.
Turn the dough onto a piece of plastic wrap and wrap the dough. Place it in the refrigerator for at least 30 minutes.
When ready to bake, preheat the oven to 350 degrees.
Take the dough out of the refrigerator and pinch of a 1 inch piece of dough. Roll the dough into a ball and place it on a baking sheet. Press your thumb into the center of the cookie to make a well. Repeat this process for the rest of the dough.
Bake for 12 minutes or until the cookies are just slightly golden brown.
Remove the cookies from the baking sheet and place them on a wire rack to cool.
While the cookies cool, microwave the Nutella in a microwave safe bowl for 15 seconds and then pour it into a gallon Ziploc bag. Cut off the end of the Ziploc bag and pipe the Nutella into the center of the cookie.