Preheat oven to 350ºF. Line a baking sheet with a parchment paper or a silicone baking mat. Set aside.
In a medium size bowl, whisk together the flour, baking soda, baking powder, and salt. Set aside.
In a separate medium size bowl with a hand held mixer or the bowl of a stand mixer fitted with a paddle attachment, cream together the butter and brown sugar on medium speed. Scrape down the sides and bottom of the bowl with a spatula. Add the egg and vanilla extract, and beat again on medium speed until everything is combined and there are no lumps.
With the mixer on low, slowly add the dry ingredients to the wet ingredients in 2 additions, mixing thoroughly after each addition. Add peanut butter chips and beat again on low until completely combined. Turn the mixer off.
Using a spoon, dollop spoonfuls of Nutella onto the cookie batter. Turn the mixer onto low and allow it to beat the cookie dough about 3-4 revolutions. The Nutella should be streaked but not blended. If you leave the mixer on too long and blend it, that is ok.
Using a cookie scoop (I use this #50 cookie scoop for all of my standard size cookies), scoop rounded balls of cookie dough. Using your hands, carefully and quickly (because the warmth of your hand will start to melt the Nutella) roll the dough into a ball. It does not need to be perfect, this is just to keep the cookie smooth. Bake for 10-12 minutes until sides just begin to brown (mine took exactly 11 minutes). Remove from oven and allow to cool on the baking sheet for 1-2 minutes before transferring to a wire rack to cool completely. As cookies cool, I pressed a few peanut butter chips into the tops of the cookies. Cookies stay fresh in an airtight container at room temperature up to 1 week. Baked cookies may be frozen up to 2 months. Balled cookie dough can be frozen, up to 2 months. Bake frozen on baking sheet for 11-13 minutes.