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