Put the cream cheese in the bowl of a stand mixer fitted with a whisk attachment (or in a large bowl if using a hand mixer) and whisk on medium speed until fluffy. Add the sugar and a pinch of salt and whisk until smooth. Add the cream and vanilla and whisk just until medium-soft peaks form. Refrigerate until firm, about 2 hours.
Line a 1 1/2-quart loaf pan with plastic wrap, leaving at least a 2-inch overhang on all sides. On the bottom of the loaf pan, lay 6 cookies face-down, overlapping slightly. Spread 3/4 cup of the whipped cream evenly over the cookies. Top with 3 heaping tablespoons of the chocolate. Repeat the layering two more times with 6 to 7 cookies. Place the last 6 to 7 cookies on the shaved chocolate. Fold the plastic wrap over the top of the loaf pan so the entire top layer is covered. Refrigerate overnight.
To serve, turn back the plastic wrap, flip the icebox cake out onto a platter and remove the plastic. Top with the reserved chocolate and serve immediately.
Sift the flour, cocoa powder, baking soda and 1/8 teaspoon salt into a medium bowl.
Beat the butter and granulated sugar in the bowl of a stand mixer fitted with a paddle attachment (or a large bowl if using a hand mixer) on medium speed just until combined. Beat in the egg yolk just until combined. Beat in the food coloring and vanilla until the color is evenly distributed, scraping down the bowl as needed. Reduce the mixer speed to low and gradually add the flour mixture. Beat just until the dough comes together. Form the dough into two 1-inch-thick disks, wrap tightly in plastic and refrigerate until firm, about 2 hours.
Preheat the oven to 350 degrees F. Line two baking sheets with parchment paper.
Lightly dust a sheet of parchment paper with flour. Unwrap one disk, place it on the paper and cover with a large sheet of plastic wrap. Roll the dough out to 1/8 inch thick. Peel off the plastic wrap and, using a 2 1/2-inch round cookie or biscuit cutter, cut the dough into rounds. Place them on the prepared baking sheets, spacing them 1 inch apart (about 12 cookies per sheet). Gather the scraps, chill until firm, roll again and cut. Repeat with the remaining disk.
Bake the cookies until brick-red and set, 8 to 10 minutes, rotating the baking sheets halfway through. Let the cookies cool on the sheets for 3 minutes, then transfer to a wire rack to cool completely.
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