Stir coffee, espresso, and 2½ tablespoons Kahlua in a wide bowl or baking dish until espresso dissolves; set aside.
In bowl of standing mixer fitted with whisk attachment, beat yolks at low speed until just combined. Add sugar and salt and beat at medium-high speed until pale yellow, 1½ to 2 minutes, scraping down bowl with rubber spatula once or twice. Add ⅓ cup of the heavy cream to yolks and beat at medium speed until just combined, 20 to 30 seconds; scrape bowl.
Set the bowl with yolks over a medium saucepan containing 1 inch of gently simmering water; cook, constantly scraping along bottom and sides of bowl with heatproof rubber spatula, until mixture coats back of spoon and registers 160 degrees on instant-read thermometer, 4 to 7 minutes. Remove from heat and stir vigorously to cool slightly, then set aside to cool to room temperature, about 15 minutes.
Whisk in remaining 4 tablespoons Kahlua until combined. Transfer bowl to standing mixer fitted with whisk attachment, add mascarpone, and beat at medium speed until no lumps remain, 30 to 45 seconds. Transfer mixture to large bowl and set aside.
In now-empty mixer bowl, beat the remaining cream at medium speed until frothy, 1 to 1½ minutes. Increase speed to high and continue to beat until the cream holds stiff peaks, 1 to 1½ minutes longer. Using a rubber spatula, fold one-third of the whipped cream into mascarpone mixture to lighten, then gently fold in remaining whipped cream until no white streaks remain. Set mascarpone mixture aside.
Working one at a time, drop half of ladyfingers into coffee mixture, roll, remove and transfer to 13 by 9-inch glass or ceramic baking dish. (Do not submerge ladyfingers in coffee mixture; entire process should take no longer than 2 to 3 seconds for each cookie.) Arrange soaked cookies in single layer in baking dish, breaking or trimming ladyfingers as needed to fit neatly into dish.
Spread half of mascarpone mixture over ladyfingers; use rubber spatula to spread mixture to sides and into corners of dish and smooth surface. Place 2 tablespoons cocoa in fine-mesh strainer and dust cocoa over mascarpone.
Repeat dipping and arrangement of ladyfingers; spread remaining mascarpone mixture over ladyfingers and dust with remaining 1½ tablespoons cocoa. Wipe edges of dish with dry paper towel. Cover with plastic wrap and refrigerate 6 to 24 hours. Cut into pieces and serve chilled. Leftovers can be stored, tightly wrapped, in the refrigerator for up to 3 days.