Mix the dough:
Sift together the flour, salt, and baking soda. In the bowl of a stand mixer fitted with the paddle attachment, cream the butter on medium-low speed until smooth, about 2 min. Add the sugar in a steady stream and mix for another 2 min. Add the egg and vanilla and mix until well combined, scraping the bowl as needed. Reduce the speed to low and add the dry ingredients in two additions, mixing just until combined. Remove 2 cups less 2 Tbs. of the dough and set aside.
Dissolve the espresso powder in the boiling water and set aside briefly to cool. Then mix the espresso and cocoa powder into the remaining dough. Reduce the mixer speed to low, add the warm melted chocolate and mix just until thoroughly combined.
Roll the pinwheel logs:
Portion each flavor of dough into three equal pieces. (For accuracy, use a scale.) Shape each piece into a 5x5-inch square on a piece of plastic wrap and wrap well. The chocolate will be thicker than the vanilla. Refrigerate the dough for 30 min. (If the dough becomes too hard, let it stand at room temperature for a few minutes before rolling).
While the dough is chilling, tear off twelve 12-inch squares of waxed paper. Roll each piece of dough into a 7x7-inch square between two sheets of the waxed paper. Without removing the waxed paper, layer the squares of dough on a baking sheet and refrigerate for 10 to 15 min. Have ready three 15-inch sheets of plastic wrap.
To shape the cookies, remove one square of the vanilla dough and one square of the chocolate dough from the refrigerator and peel off the top sheet of waxed paper from each. Invert the chocolate square over the vanilla square (or vanilla can go on top of chocolate; try some of each for variety), taking care to align the two layers as evenly as possible. Using your rolling pin, gently roll over the dough to seal the layers together. Peel off the top layer of waxed paper.
Starting with the edge of the dough closest to you, carefully curl the edge of the dough up and over with your fingertips, so no space is visible in the center of the pinwheel.
Using the waxed paper as an aid, continue rolling the dough into a tight cylinder. After the cylinder is formed, roll it back and forth on the counter to slightly elongate it and compact it. Transfer the log to the plastic wrap, centering it on the long edge closest to you. Roll tightly, twisting the ends of the plastic firmly to seal. With your hands on either end of the log, push firmly toward the center to compact the dough. It should be about 9 inches long and 1-1/2 inches thick. Repeat with remaining dough. Refrigerate the logs until firm enough to slice, about 3 hours, or freeze for up to three months.
Bake the cookies:
Position racks in the upper and lower thirds of the oven. Heat the oven to 350°F. Line two rimmed baking sheets with parchment. Working with one log at a time, use a sharp, thin-bladed knife to slice the dough into 3/16-inch rounds. Set the rounds about 1 inch apart on the prepared pans and bake until the tops of the cookies feel set, 12 to 14 min. (don’t let the edges become too brown). To ensure even browning, rotate the sheets as needed during baking. Let the baked cookies stand for 1 minute on the pan. While they’re still warm, use a thin metal spatula to transfer them to racks. When cool, store between sheets of waxed paper in an airtight container for up to two weeks, or freeze for up to three months.