Cream: Beat the butter and sugar for 2 to 3 minutes until light and fluffy.
Eggs and vanilla: Add the eggs one at a time, then the vanilla.
Dry ingredients: Whisk the flour, baking powder, and salt. Add to the butter mixture and mix on low until a soft dough forms.
Split: Divide the dough in half. Mix the cocoa powder into one half (add 1 to 2 teaspoons milk if dry).
Chill: Shape each dough into a flat rectangle, wrap, and chill 30 minutes.
Roll out: Roll each dough between parchment into a 12 x 16-inch rectangle, about ⅛ inch thick.
Stack: Flip the chocolate dough onto the vanilla dough and gently press together.
Roll up: Cut the stack in half. Tightly roll each half into a log, starting at a long side.
Chill logs: Wrap and chill at least 2 hours, until firm.
Preheat: Heat the oven to 350°F and line baking sheets with parchment.
Slice: Slice the logs into ¼-inch cookies and place 1 inch apart.
Bake: Bake 8 to 10 minutes, until just set. Cool 5 minutes on the pan, then move to a wire rack.