In a large mixing bowl, cream together the softened butter, granulated sugar, and brown sugar until light and fluffy (about 3-4 minutes with an electric mixer). Add the vanilla extract and eggs one at a time, beating well after each addition.
In a separate bowl, whisk together the all-purpose flour, baking soda, and salt. Gradually add the dry ingredients to the wet mixture, stirring just until combined. Avoid overmixing to keep the dough tender.
Gently fold in the semi-sweet chocolate chips, distributing them evenly throughout the dough.
Cover the dough and chill it in the refrigerator for at least 30 minutes to prevent spreading and ease handling.
Take about 2 tablespoons of dough and flatten it into a disc. Place about 1 teaspoon of Nutella in the center. Wrap the dough around the Nutella, sealing it completely and rolling into a smooth ball. Repeat with remaining dough and Nutella.
Preheat oven to 350°F (175°C). Line a baking sheet with parchment paper or silicone mat. Place dough balls about 2 inches apart. Bake for 10-12 minutes until edges are golden and centers look soft.
Allow cookies to cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely, letting the Nutella center set but remain gooey.