Beat butter and sugar until creamy, then beat in egg and vanilla. Whisk flour, baking powder and salt and mix into the butter just until combined.
Divide the dough equally. Knead cocoa and milk into one half, leaving the other half plain. Roll each between parchment into a rectangle about 8 by 12 inches.
Lay the chocolate rectangle over the vanilla rectangle and remove the upper parchment. Roll tightly from a long edge into a 12-inch log, using the lower parchment to help; wrap and refrigerate for 2 hours, additional to active time.
Heat the oven to 350°F and line two baking sheets. Slice the cold log into 36 rounds about 1/3 inch thick and place 1 inch apart.
Bake one sheet at a time for 11 to 12 minutes, until the pale edges are lightly golden. Cool on the sheets for 5 minutes, then transfer to racks.