Add instant espresso powder to hot water and whisk until dissolved. Add in coffee liqueur and vanilla extract and whisk to combine.
Add the butter and cream cheese to a mixing bowl and beat on medium speed until no lumps remain. Add in the powdered sugar and continue mixing until well combined. Add in 3 tablespoons of the coffee liqueur mixture from step 1 and beat until smooth.
Dust the bottom of a 9x9" baking dish with a thin layer of cocoa powder.
Brush each ladyfinger twice on each side with the coffee liqueur mixture. Start with just eight ladyfingers (wait to brush the rest until the next layer so they don't get too soggy). Place the ladyfingers flat side down on the bottom of the baking dish, covering it in an even layer.
Spread ⅓ of the cream mixture over the ladyfingers in an even layer. Repeat with two more layers of ladyfingers and cream. Spread the final layer of cream thinly over the top of the ladyfingers, just covering them.
Use the remaining 1 cup of cream from the refrigerator to pipe atop the tiramisu. Refrigerate for at least 4 hours, or overnight before serving. Just before serving, dust the top of the tiramisu with cocoa powder. Slice and serve.