Sift the flour, baking powder, and salt together and set aside.
In a mixer with a paddle attachment cream the butter well; then add the sugar and continue creaming until light and fluffy. Add the eggs 1 at a time and then the vanilla.
On the low setting, add the dry ingredients and mix just until combined. Divide the dough in half and return half the dough to the mixer. Add the warm melted chocolate and mix to combine. Shape both pieces of dough into 4 by 4-inch square, and wrap them in plastic wrap and chill for 30 minutes.
Cut each square into 4 strips then place them on a sheet pan and keep chilled while you roll out the dough. Between pieces of parchment paper, roll out a piece of chocolate dough into a rectangle 6 by 7 inches (have a ruler nearby). Roll a piece of vanilla dough out into a 6 by 6-inch square. Peel off the top pieces of parchment from both doughs and flip the vanilla dough onto the chocolate, allowing 1/2-inch border of chocolate dough around the top and bottom. Press the 2 doughs together lightly with a cake pan or other flat pan. Peel off the top piece of parchment and fold the 1/2-inch of over hanging chocolate dough up and over the vanilla dough. Use the parchment to roll up the dough into a tight pinwheel. Wrap in plastic wrap and chill 4 to 5 hours (roll the dough a couple times the first hour so it doesn't develop a flat side). Repeat with the remaining pieces of dough.
Preheat the oven to 350 degrees F.
Butter a sheet pan. Unwrap the roll and cut into 1/4-inch slices. Place them 1 1/2 inches apart on the sheet pan and bake for 9 to 11 minutes.