Preheat your oven to 180°C (350°F) to ensure even baking.
In a mixing bowl, cream the softened butter and powdered sugar together using an electric mixer or whisk until light and fluffy, about 3-4 minutes.
Add the large egg and vanilla extract to the butter-sugar mixture and mix until well incorporated.
In a separate bowl, whisk together the flour, corn starch, cocoa powder, ginger powder, and a pinch of salt.
Gradually add the dry ingredients to the wet ingredients and mix until just combined, avoiding over-mixing for tender cookies.
Pour in the cold milk and mix until the dough comes together; it should be slightly sticky but manageable.
Gently fold in the chopped dark chocolate or chocolate chips for delightful melted pockets.
Form the dough into small balls using your hands or a cookie scoop, place them on a parchment-lined baking sheet, and flatten slightly.
Bake the cookies for 12-15 minutes until edges are set and tops are slightly cracked. They will firm up as they cool.
Remove from oven and cool on the baking sheet for a few minutes, then transfer to a cooling rack. Enjoy warm or at room temperature.