Combine the espresso, coffee liqueur, 2 tablespoons sugar, 1/4 cup Marsala and 1/4 cup water in a medium bowl and whisk until the sugar dissolves.
Beat the mascarpone in a bowl to loosen it up, then set aside.
Beat the cream, vanilla, remaining 1/4 cup sugar and remaining tablespoon Marsala together in a clean bowl with an electric mixer until it just holds stiff peaks. Fold the mascarpone into the whipped cream mixture.
Working one at a time, briefly dunk half of the ladyfingers in the espresso mixture and use them to line the bottom of a 9-by-13-inch baking dish, breaking or trimming the cookies as necessary. Spread half of the mascarpone mixture evenly on top. Dunk and arrange the remaining ladyfingers on top of the mascarpone, then spread with the remaining mascarpone.
Cover the tiramisu and refrigerate until the ladyfingers have softened and the flavors have blended, at least 5 hours and preferably overnight. Dust with cocoa powder before serving.