Chop the white chocolate and dark chocolate into rough chunks and set aside.
Using a freestanding mixer or a handheld electric whisk, beat together the room-temperature butter, light brown soft sugar and golden caster sugar together for 2 minutes, until light and fluffy.
Beat in the egg and vanilla extract. Add in the plain flour, bicarbonate of soda, baking powder and sea salt. Beat on a low speed until just combined.
Stir the chocolate chunks through and bring the dough together using your hands or a wooden spoon. Chill for an hour to firm up.
Preheat the oven to 180°C, Fan 160C, gas 4. Spoon the cookie dough into a non-stick frying pan and roughly flatten using the back of a spoon. Bake for 20 minutes, until pale golden.
Leave to cool for a few minutes (being cautious of the hot frying pan handle) before serving on the centre of the table with scoops of ice cream in the middle.
Notes
The ultimate party crowd pleaser. Very indulgent but go the whole hog and serve with ice cream. Just remember to allow an hour for the dough to chill.