When ready to assemble the cake, combine the milk, Grand Marnier (if using), and espresso and set aside.
Place the cream, crème fraîche, powdered sugar, vanilla extract, and cinnamon in the bowl of the stand mixer with the whisk attachment in place. Whisk on medium-high speed until soft peaks form—be careful not to over-whip, as the cream will thicken as you spread it.
Transfer 2 cups of the mixture to a small bowl and refrigerate—this will be used to finish the cake. Pipe or dollop a roughly 12-inch/30cm-long line (about ¾ inch/2cm wide) of the remaining cream mixture down the center of a long cake plate or board—this is to help position the cookies for assembly.
Take 20 of the cookies and, working with one cookie at a time, lightly brush both sides with the milk mixture—you want to just moisten the entire cookie without drenching it. Then, using a small spatula or knife, spread 2 tablespoons of the cream on one side of the cookie. Standing the cookie upright, press it down onto one end of the strip of cream.
Repeat with another cookie, then place alongside the first cookie, pressing to sandwich them together. Continue with the remaining cookies to form a long log cake. Spread the remaining cream mixture over the top and sides of the log—don’t worry if it only barely covers the cake, as it will be topped up with the reserved cream the following day. Cover loosely and refrigerate for at least 6 hours or overnight.
About 15 minutes before you’re ready to serve, combine the strawberries in a bowl with the sugar, finely shaved orange zest, and Grand Marnier. Allow to macerate for 10–15 minutes.
Meanwhile, spread the reserved cream over the top and sides of the log.
When ready to serve, tumble about half the strawberries along the top of the cake, pressing them on slightly to help them stick. Drizzle any syrup over and around the plate. Finish with the orange zest strips on top. When serving, slice on the diagonal—warming the blade of the knife with hot water helps with the cleanness of the slice—to reveal the stripes.