Preheat oven to 190 degrees C. Line a baking tray with a silicon baking mat or baking paper.
Mash the butter, white sugar and brown sugar together in a large mixing bowl with a spatula until creamy and smooth, 2 to 3 minutes. Add the egg and vanilla; whisk vigorously for 20 to 30 seconds.
Whisk the flour, salt and bicarb soda together in a small bowl; dump into the butter mixture and mix until just combined. Fold the dark chocolate bits, white chocolate bits and milk chocolate bits into the mixture. Arrange onto the prepared baking tray using a small scoop or large spoon.
Bake in the preheated oven until golden brown, about 10 minutes; remove from oven and allow to cool on the tray for 10 minutes. Transfer to a wire rack to finish cooling completely.
The amounts of chocolate bits can be doubled for extra-decadent bickies.