Line a small baking sheet or plate with parchment paper or wax paper. Dollop or pipe the nutella into small ½ inch circles, until you get 12 total. Place in the freezer for at least an hour.
Preheat the oven to 350F. Line two baking sheets with parchment paper or silicone baking mats. Set aside. In a medium mixing bowl, combine gluten-free flour blend, xanthan gum (if using), baking powder, and baking soda. Whisk to combine. Set aside.
In a large mixing bowl, add the softened butter, peanut butter, brown sugar and light sugar.
Cream with an electric mixer for 2-3 minutes, until light and fluffy, scraping down the sides of the bowl with a spatula as needed.
Add the vanilla extract, egg and salt. Mix until smooth.
Add half of the flour mixture to the butter mixture and stir until just combined.
Repeat with the remaining flour, stirring until no more streaks of flour remain.
Stir in the chocolate chunks until combined.
Using a 2-3 tablespoon cookie dough scoop, fill the scoop halfway full with cookie dough. Then, press a frozen nutella chunk into the cookie dough until it is submerged. Fill the scoop the remaining way with cookie dough so that the nutella is completely covered.
Place dough on the prepared baking sheet and repeating with remaining cookie dough and nutella.
Bake at 350F for 10-12 minutes, until the edges are just set.
Remove from the oven and immediately sprinkle with flaky sea salt. Let cool before serving.