Almond and chocolate work exceptionally well together -- especially when creating cookie dough swirls.
Put butter and sugar in the bowl of an electric mixer fitted with the paddle. Cream on medium-high speed until fluffy, 2 to 3 minutes. Mix in eggs and salt. Add vanilla, milk, flour, and cocoa; mix until incorporated.
Wrap dough in plastic wrap; gently flatten into a rectangle. Refrigerate until firm, about 1 hour or up to 1 day.
On a generously floured 12-by-26-inch sheet of parchment paper, roll out chocolate dough into a 10-by-24-inch rectangle, dusting with flour as needed and occasionally lifting dough with an offset spatula to prevent sticking. Refrigerate.
On another generously floured 12-by-26-inch sheet of parchment paper, roll out almond dough into a 9-by-20-inch rectangle, as described above.
Lightly brush chocolate dough with egg white. Gently stack almond dough on top. Starting with one short side, roll doughs together into a log, gently lifting parchment as you go. Lightly brush edge with egg white; seal seam by pinching and pressing gently. Wrap log in parchment or waxed paper. Chill in freezer until firm, about 1 1/2 hours.
Preheat oven to 350 degrees. Line baking sheets with parchment paper. Let dough stand at room temperature 10 minutes. Using a serrated knife, cut log into 1/4-inch-thick rounds, rotating after each cut to keep it round. Transfer to sheets. Bake until set (not brown), 18 to 20 minutes. Let cool on parchment on wire racks.