Preheat the oven to 180°C (356°F). Line a large baking tray with baking paper.
In a large bowl, beat 150 g room-temperature butter with 100 g powdered sugar until the mixture is light, airy, and creamy.
In a separate bowl, whisk together 200 g flour, 50 g corn starch, 2 tbsp cocoa, 1 tsp ginger powder, and 1 pinch of salt.
Add 1 large egg and 1 tsp vanilla extract to the butter–sugar mixture and mix until fully incorporated.
Gradually add the dry ingredients to the wet mixture and mix on low speed (or fold with a spatula) until a cohesive dough forms.
If the dough is too stiff to roll or cut, add the 2 tbsp cold milk gradually, 1 tbsp at a time, until the dough is workable but not sticky.
Place the dough between two sheets of baking paper and roll to about 3–5 mm thickness. Use a pastry cutter to cut rounds and place them on the prepared tray, leaving 2–3 cm between each cookie. Gather any scraps, re-roll once, and cut more rounds.
Bake for 10–12 minutes, until the edges are just lightly browned. Do not overbake.
Remove the tray from the oven and let the cookies rest on the tray for 2–3 minutes, then transfer them to a cooling rack to cool completely.
Chop 100 g dark chocolate and melt it in a heatproof bowl over a simmering pan of water (bain-marie) or in the microwave in short bursts, stirring between bursts, until smooth. Decorate the cooled cookies with the melted chocolate (drizzle or dip) and let the chocolate set before serving.