Combine the flour, cocoa powder, baking soda, and salt in a medium bowl, aerating to mix with a fork.
Add the butter to the bowl of a mixer and beat until fluffy and creamed. Add both sugars and the vanilla to the bowl and cream together on medium-high for about a minute.
Turn the mixer to low and add the milk, stirring until combined nicely.
Gradually add the flour with the mixer continuing on low until just mixed. The cookie dough will be quite stiff.
Empty the dough into a piece of wax paper or plastic wrap and using the paper or wrap, form the dough into a log about 10” long. Avoid overworking the dough; use the paper/plastic to do the work of pulling the dough together and square up the ends. Wrap tightly and refrigerate for 45 minutes up to 3 days.
When ready to bake, preheat the oven to 350° F (176° C) with a rack set in the middle. Grease a cookie sheet lightly, line with parchment paper, or line it with a silicone mat.
Remove the dough from the fridge, unwrap, and with a serrated knife slice the dough into scant 1/4” rounds using a sawing motion to avoid flattening the circles. Place the rounds on the cookie sheet about an inch apart and bake for 10-12 minutes, rotating the cookie sheet halfway through the baking time.
The cookies will puff and crackle a bit, the edges will look mostly set and drier when ready. They'll deflate and level out as they cool.
Let the cookies cool about 2-5 minutes to firm up a bit then remove them to a cooling rack and continue baking.