Line a tray with parchment paper. Scoop 1 tbsp portions of Nutella onto the tray and freeze until solid, about 30 minutes.
To a saucepan, add the butter. Cook over medium heat until the butter foams and turns golden brown with brown specks. Transfer to a bowl and let cool to room temperature. This takes around 5 minutes. Watch carefully because the butter will burn easily.
In a bowl, whisk together the browned butter, brown sugar, and white sugar until smooth and glossy.
Add the egg and vanilla extract. Whisk until fully incorporated.
In a separate bowl, whisk together the flour, baking soda, and salt.
Fold the dry ingredients into the wet ingredients until just combined.
Fold in the chocolate chips.
Preheat the oven to 350°F.
Scoop the dough into equal portions. Flatten each piece of dough, place a frozen Nutella scoop in the center, then seal and roll back into a ball.
Place the cookie dough balls onto a parchment-lined baking tray.
Bake for 10–14 minutes, depending on the size of the cookies.
Sprinkle with flaky salt while warm and let cool slightly before serving.