Place a small pot filled with 2-inches of water over high heat and bring to a boil. Reduce the heat to low. Place the chopped chocolate in a heat-proof bowl and set over the bot, making sure the bowl doesn’t touch the water.
Stir until the chocolate is fully melted. Turn off the heat and remove the bowl from the pot.
In a large bowl, whisk together flour, baking powder, and salt.
In the bowl of a stand mixer fitted with a paddle attachment, add the butter and sugar. Beat on medium-high until light and fluffy, about 3 minutes.
With the mixer on low, add the eggs, one at a time, until fully incorporated. Stop to scrape down the sides of the bowl as necessary. Beat in the vanilla.
With the mixer on low, slowly add flour mixture, and mix until fully incorporated. Divide the dough in half, leaving one half in the mixing bowl.
With the mixer on low, add the melted chocolate to the dough left in the bowl, and mix until fully incorporated.
Place each dough on separate sheets of parchment paper and press into ½-inch-thick square. Place another piece of parchment on top of each dough and roll dough out into 13x9-inch rectangles. Refrigerate the doughs until firm but pliable, about 30 minutes (If the dough becomes too firm, let them rest at room temperature until they become pliable).
Remove the top piece of parchment from each dough rectangle. Flip the chocolate dough on top of the plain dough, lining up the edges as best you can, and remove the remaining parchment piece.
Starting from one long side, roll the dough up, jelly-roll style, using the bottom parchment as a guide. Tightly cover the dough roll in plastic wrap, and twist the ends until tight (this gently presses the dough together and gets rid of any airspace that may still be inside the log). Refrigerate for at least 2 hours or until firm.
Preheat the oven to 375F. Line 2 baking sheets with parchment paper.
Unroll the chilled dough and trim the edges, making a 12-inch-long log. Carefully slice half of the log into 24 cookies (about ¼-inch-thick slices) with a sharp knife. Wrap remaining dough and place in the refrigerator until ready to use. Place cookies 1½ inches apart on the prepared baking sheets.
Bake for 7 to 8 minutes or until the edges just start to brown. Let the cookies cool for 2 minutes on the pans, and then transfer to a wire rack to cool completely. Repeat the process with the remaining half of the dough.
