Load all of the dry ingredients, including the chocolate splinters, into a food processor and pulse to combine.
Cut the butter into tablespoon-sized pats and add to the processor and pulse until the butter is broken up very finely and well incorporated (kind of like making a crumble/crisp).
In a liquid measuring cup, whisk together the milk and vanilla and, with the processor going, slowly stream it in. Let it mix for only a minute or so, just until it resembles cookie dough.
Turn it out onto a lightly floured surface and roll into a log, about 1 ½” in diameter (about 12” long). Wrap in plastic wrap and chill in the freezer on a tray for at least 1 hour. If you’re going to serve these whole you may want to take it out after 10 minutes or so and roll it to round it better on all sides (obviously the underside that sits on the tray will flatten). If, however, you’re making them for some rubbly crumble then don’t worry.
Preheat the oven to 350°
Unwrap the dough onto a wooden cutting board and slice into ¼” thin discs. The way I do this, to make sure that I get the right amount of wafers, is by cutting the log in half (each half yielding 24 wafers). Both halves are cut in half again, and then each piece is cut in half again. Then I use a sharp pairing knife to cut each section of the dough into 6 discs. Maybe this is simple to you but I have to talk myself through it—sad but true.
Line 2 baking sheets with parchment paper and bake 12 wafers per sheet for 12 – 15 minutes—until they’re crisped and set.
Remove from the oven and allow them to cool slightly on the trays before moving them to cooling wracks for their final cooling. They will look and feel a little soft but as they cool they crisp up and harden further.
-Make sure to use Dutch-processed cocoa powder. It has a deeper flavor and color than regular (natural) cocoa powder, and because it's been treated with an alkaline solution to remove the natural acidity, it won't react with the baking soda, making it act as a levener. And no, you can't just leave out the baking soda because you need it to get the right texture on these.