Line a baking sheet with wax paper and use a teaspoon to turn 3/4 cup of the Nutella into 24 teaspoon-sized dollops. Because of the nature of the Nutella, dollops do not need to be exact measurements or all the same size, you just need 24. Freeze for 30 minutes.
While Nutella is freezing, preheat the oven to 350 degrees F and line cookie sheet with parchment paper and set it aside.
Cream the butter, remaining 1/2 cup Nutella, and sugars together until smooth. Then add in the pudding, eggs, additional egg yolk, and vanilla and beat for about one minute on medium speed.
In a separate bowl, whisk together the flour, baking soda, and salt, then add the dry ingredients to the wet ingredients a ½ cup at a time and mix until combined.
Mix in the chocolate chips just until incorporated.
Once the dough is ready and the Nutella dollops are frozen, use a medium cookie scoop to scoop out a scoop of the cookie dough, press a Nutella dollop into the flat part of the dough, scoop out another scoop and press the flat side against the other ball of dough, sandwiching the Nutella between them. Roll between your hands to seal the Nutella in.
Place cookie dough balls 2 to 3 inches apart on the prepared cookie sheet and bake for 13 to 15 minutes. Cookies may require a little longer than this depending on your oven, the center will be gooey because of the Nutella but the edges should start to crisp up and the top should begin to crack.
Allow the cookies to cool on the baking sheet for a couple of minutes before transferring to a cooling rack.