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To make the cookies: In a medium mixing bowl, sift or whisk cocoa powders to eliminate any clumps. Add the flour, espresso powder, salt, and baking powder and whisk to combine.
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In a large mixing bowl or the bowl of your stand mixer, beat the butter until smooth, 1 to 2 minutes. Add the sugar, then beat on medium speed until well-combined and lightened in color, 1 to 2 minutes. Add the egg and vanilla, and beat until homogenous, about 30 seconds to 1 minute. Add the dry ingredients and mix just until combined. Transfer the dough to a sheet of plastic wrap or parchment, shape into a flat square about 1" thick, cover, and refrigerate until firm, at least 1 to 2 hours. This step can be done up to a few days in advance; if the dough is chilled overnight, it may need to soften at room temperature for about 5 to 10 minutes before rolling.
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When you’re ready to bake, preheat the oven to 325°F with racks in the upper and lower third.
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On a floured surface with a floured rolling pin, roll out dough to 1/8" thick. (For extra insurance against sticking, roll out your dough on a piece of floured parchment, lifting and flouring it if it starts to stick. If the dough is getting too soft, transfer it to the fridge and come back to it later.)
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Using a sharp knife or pastry wheel, cut the dough into 1 1/2" squares (no need to be exact — slightly bigger or smaller is just fine). Arrange cookies on two baking sheets lined with parchment (the cookies can be fairly close together as they won’t spread dramatically). Chill the dough in the fridge or freezer while you reroll any scraps and cut more squares. You should get between 45 and 50 cookies total.
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Bake for 15 to 16 minutes, rotating the pans once halfway through. The cookies are done when the tops are matte and feel set. Allow them to cool completely on sheets. The cookies will firm up as they cool.
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To make the cream filling: In a large mixing bowl or the bowl of your stand mixer, combine the cream, confectioners’ sugar, espresso powder, vanilla, and salt. Use the whisk attachment to whip the cream just until stiff peaks form, 3 to 4 minutes on medium speed. Take care not to overbeat — the cream will deflate and become dense.
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To assemble the cake: Line an 8 1/2" x 4 1/2" or 9" x 5" loaf pan with a loaf pan lifter or plastic wrap so that there are several inches of excess hanging over all sides.
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Use a flexible spatula or extra-large cookie scoop to portion about 1/2 cup of the whipped cream into the bottom of the loaf pan. Use a small offset spatula or the back of a spoon to smooth the cream into a layer about 1/2" thick. Arrange the cookies in a single layer on top of the cream (you should be able to fit about 8 cookies snugly in a 4 x 2 arrangement). Top with a thin layer of cream, followed by another layer of cookies. Repeat this layering process until you’ve reached the top of the pan and used up all (or nearly all) of the cookies. Finish with a layer of whipped cream.
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Cover the cake and chill, in the pan, for at least 24 hours in the refrigerator, which will give the cookies a chance to soften completely. (Any leftover cookies and cream are the baker’s treat!)
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To serve: Uncover the cake, invert it onto a cutting board or serving plate, and gently remove the loaf lifter or plastic wrap. If you’re a perfectionist, use an offset spatula, bench knife, or metal spatula that’s been run under hot water and then dried to smooth out the whipped cream and cover any bare cookies.
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To garnish: Use a vegetable peeler to shave the chocolate bar into small curls over the surface of the cake, if desired. For the neatest slices, use a sharp chef knife that’s hot but dry to cut the cake.
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Storage information: Store cake, covered, in the refrigerator for up to 3 days.
