Using a stand mixer with the balloon whisk attachment on medium-high speed, whisk the caster sugar, eggs, and vanilla together until thick ribbons of the mixture form when you lift the whisk from the bowl, 5 to 7 minutes.
Add the cooled, toasted milk powder and the dark brown sugar to the browned butter and roughly mix it together.
In a separate large bowl, whisk the flour, baking soda, and fine flaked salt together until combined.
Add the buttery mixture to the egg mixture, a spoonful at a time, and fully incorporate before adding the next one.
If using a free standing mixer, switch the attachment to the paddle. Add the flour mixture to the wet ingredients in three stages, incorporating the flour until no dry patches are visible with each addition. Add the final third of the flour by hand, together with the chopped chocolate, mixing with a wooden spoon.
Cover the dough and chill in the fridge for at least 2 hours, or overnight. You can keep the dough refrigerated like this for up to three days. If chilling overnight, remove the dough from the fridge 45 minutes before baking.
When ready to bake, preheat the oven to 340°F (170°C) and line 2 large rimmed baking sheets with parchment paper.
Using an ice-cream scoop, shape 2 ounce (57 g) balls of dough and place on the lined baking sheets, leaving at least 1 1/2 inches (4 cm) space between each cookie to allow for spreading.
Bake until they are golden brown but not too crisp, 11 to 15 minutes. As soon as they come out of the oven, sprinkle a good amount of flaked salt on top and leave to cool on the baking sheets.
Store in an airtight container for up to a week.