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Step 1
In the bowl of a food processor fitted with the metal blade, add the flour, cocoa powder, sugar, salt, and baking soda. Pulse the ingredients a few times to combine thoroughly. Dollop the butter around the dry ingredients and pulse a few more times until the butter starts to incorporate and large chunks begin to form. Mix the milk and vanilla together in a small bowl. With the mixer running, pour the milk mixture into the feeding tube in a slow and even stream until the cookie crumb mixture starts to form together and ball up on the sides of the bowl.
Step 2
Transfer the cookie dough to a work surface and knead it a couple of times to fully incorporate all of the ingredients. Divide the dough in half and shape each half into a long and narrow log, about 1 ¼ inches to 1 ¾ inches in diameter. Depending on how large you want your wafer cookies to be will determine how thick to form the log. Wrap each log in plastic wrap and refrigerate for at least 2 hours or up to a week.
Step 3
Position the oven racks to the upper and lower thirds of the oven. Preheat oven to 350° F. Line baking sheets with parchment paper.
Step 4
Slice the dough logs into approximately ⅛-inch thick slices and lay the dough rounds on the baking sheets about 1 inch apart. I formed my dough into 1 ¼-inch diameter logs and was able to fit 24 cookies on each of my baking sheets.
Step 5
Bake for 10-12 minutes, rotating pans from back to front and top to bottom halfway through the baking time. The cookies will be finished baking about 1 ½ minutes after the puffed-up dough deflates so try to keep an eye on them. Cool the cookies on the baking sheets on wire racks for 5 minutes then transfer the cookies to the racks to cool completely – they will crisp up as they cool.