Using a stand mixer fitted with the paddle attachment, beat the butter, caster sugar, brown sugar, and vanilla on medium speed until light and fluffy, about 3 to 5 minutes.
Scrape down the bowl. With the mixer running on low, slowly add the flour and toasted milk powder until just combined. Add the chopped chocolate and mix briefly until evenly distributed. The dough will be stiff.
Divide the dough in half. Roll each half into a log roughly 5.5 to 6 cm / 2¼ inches in diameter.
While the dough is still soft and pliable, brush each log with beaten egg and roll firmly in the demerara sugar to form an even crust.
Wrap each log tightly in cling film and refrigerate for at least 2 hours until firm, or freeze at this stage for later use.
When ready to bake, preheat your oven to 180°C / 350°F and line a large baking sheet with baking paper.
Using a sharp knife, slice the logs into rounds about 1.2 cm / ½ inch thick. Place on the prepared tray with space between each cookie.
Bake for 12 to 15 minutes until the edges are just beginning to turn golden brown. The centres will look slightly underdone, which is correct. They firm up as they cool.
Allow to cool on the tray for 5 minutes before transferring to a wire rack.