Bring 2 1/2 cups water to boil in a small saucepan. Add the sugar and stir until dissolved. Remove from the heat and stir in the espresso powder and coffee liqueur. Pour into a shallow bowl or dish and let cool completely.
Beat the mascarpone and confectioners' sugar with an electric mixer on medium speed just until smooth and light (do not over beat, or it will separate), about 20 seconds. Beat the cream on medium-high in a second bowl to form soft peaks. Fold 1/3 of the whipped cream into the mascarpone to lighten it, then gently fold in the remaining whipped cream.
Working with a couple at a time, dip half the ladyfingers in the espresso mixture until moistened but not falling apart, about 5 seconds per side. Put them snugly in rows in the bottom of an 8-by-8-inch glass or ceramic baking dish.
Spread half of the mascarpone mixture over the layer of ladyfingers and sprinkle with all of the chopped or shaved chocolate. Repeat soaking and layering with the remaining half of the ladyfingers. Spread the remaining mascarpone mixture smoothly over the top. Cover with plastic wrap and chill at least 4 hours or up to overnight.
To serve, remove the plastic wrap and smooth the mascarpone cream layer again, if necessary. Dust the top of the tiramisu with cocoa powder. Cut into squares and serve.