Scoop out 26 1-tsp. sized scoops of Nutella onto a parchment lined baking sheet. Freeze until solid, about 1 hour.
Preheat the oven to 350º and line large baking sheets with parchment paper.
In a medium bowl whisk together the flour, baking soda, baking powder, and salt.
In a large bowl, use an electric mixer to beat the butter and sugars on medium-high speed until smooth, 1 to 2 minutes. Beat in the peanut butter until fully combined. Beat in the egg and then the vanilla. On low speed gradually add the flour mixture.
Drop 2-Tbsp. sized balls of dough onto the prepared baking sheets, spacing 2-inches apart. Using your hands, break each ball of dough into two pieces and place a teaspoon of frozen Nutella in between. Form the dough around the Nutella, making sure the edges are sealed. Using a large fork, slightly flatten the dough and make a criss-cross pattern with the tines.
Bake for about 12 minutes or until slightly browned. Allow the cookies to cool on the pan slightly before transferring to a wire rack to cool completely. Serve or store in an airtight container at room temperature for up to 4 days.