In a large bowl, combine the flour, baking powder and salt. Set aside.
Using a stand mixer on medium-low speed, mix the butter until smooth and creamy. Add the sugar in 4 additions and mix for 2 minutes. Add 2 of the eggs, then the vanilla extract, mixing for 1 minute. Stop the mixer and scrape down the side of the bowl as needed. Reduce the speed to low and add the dry ingredients in 3 additions, blending just until combined. Do not over mix.
Divide the dough in half and blend the warm, melted chocolate into half of the dough, mixing thoroughly without overworking the dough. Shape each flavor of dough into a 4-by-5-inch rectangle. Wrap each piece in plastic wrap and refrigerate for 1 hour, or until firm enough to roll.
In a small bowl, lightly beat the last egg with 2 teaspoons of water.
Divide each chocolate and vanilla rectangle lengthwise into 4 strips, for a total of 8 strips. Place the strips on a piece of plastic wrap. Working with 2 strips of each flavor at a time, brush the exposed cut side of the strips lightly with the egg wash. Place a vanilla strip alongside a chocolate strip, using the egg wash to hold them together. On top of each one, place a strip of the opposite flavor. Rotate back and forth with your hands to seal the 4 strips together. Roll in plastic wrap, twisting the ends tightly to form a cylinder. Repeat, using the remaining chocolate and vanilla strips. Chill for several hours or up to 3 days, or freeze for up to 1 month.
Preheat the oven to 350 degrees. Position the oven racks in the upper and lower thirds of the oven. Lightly coat 2 baking sheets with nonstick spray oil.
Unwrap one cylinder at a time and place it on a cutting board. Using a thin, sharp knife, cut the roll into 3/16-inch slices. Place the slices about 11/2 inches apart on the baking sheets. (To make Bow Ties, gently pinch opposite sides together after the slices are on the baking sheet. You can pinch either the chocolate or vanilla side, or some of each. The more you pinch, the greater the definition, but be careful not to separate the dough.) Bake for 9 to 11 minutes, or until the edges just begin to brown. To ensure even browning, toward the end of baking time, rotate the pans top to bottom and front to back. Remove from the oven, let stand 1 minute, then loosen with a thin spatula while the cookies are still hot. Transfer to racks to cool completely. Store in an airtight container, layered between strips of wax paper, at room temperature for up to 3 weeks, or freeze.