Melt 1 cup of butter in a pan over medium heat. Keep an eye on it, stirring now and then, until it turns golden and smells nutty (about 5–7 minutes). Let it cool completely.
In a big bowl, whisk the white sugar, brown sugar, and eggs together until the mix looks fluffy and pale. This takes about 2 minutes by hand or 1 minute with a mixer.
Pour in the cooled brown butter and vanilla. Stir until the mixture is smooth and shiny.
Add the sifted flour a bit at a time. Mix gently until just combined. If the dough feels too sticky, add a tablespoon of flour at a time until it firms up.
Fold in 1 cup of semi-sweet chocolate chunks. Stir just enough to spread them out evenly.
Line a pie pan with parchment or lightly grease it. Press half the dough into the bottom and slightly up the sides.
Spread a thick layer of Nutella over the dough. Leave a little space around the edges so it doesn’t leak out.
Spoon the rest of the dough on top. Gently spread it to cover the Nutella completely and press the edges to seal. Sprinkle extra chocolate chunks if you like.
Bake at 350°F (180°C) for 35–40 minutes. The edges should be golden, and the middle soft but set.
Let it sit for 20 minutes before slicing. Serve warm with a scoop of ice cream or a drizzle of chocolate.