Combine the cooled espresso and coffee liqueur (if using) in a shallow dish. Set aside.
In a heatproof bowl set over a pot of gently simmering water (double boiler), whisk the egg yolks, sugar, and milk together. Cook, whisking constantly, for 8-10 minutes until the mixture thickens and reaches 160F (71C). Remove from heat and let cool to room temperature, whisking occasionally.
Whisk the mascarpone into the cooled egg mixture until smooth and well combined.
In a separate bowl, whip the heavy cream to stiff peaks. Gently fold the whipped cream into the mascarpone mixture in two additions until no streaks remain.
Quickly dip each ladyfinger into the coffee mixture for about 1 second per side (do not let them get soggy), then arrange in a single layer in the bottom of a 9x13-inch dish.
Spread half of the mascarpone cream evenly over the ladyfingers. Repeat with a second layer of dipped ladyfingers and the remaining mascarpone cream, smoothing the top.
Cover and refrigerate for at least 4 hours, preferably overnight, to let the layers set and the flavors meld.
Just before serving, dust the top generously with cocoa powder. Slice and serve chilled.