Line the base and sides of a 7cm deep, 10cm x 21cm loaf pan with baking paper, extending it 2cm up all sides. Place in the freezer to chill while getting the remaining ingredients ready.
Peel and dice 2 mangoes. Spoon the vanilla ice cream into a bowl and fold through diced mango. Spoon into the loaf pan and smooth the surface. Cover and freeze for 1 hour.
Mix the espresso powder and boiling water together in a shallow dish, stir in the liqueur. Dip 1 biscuit at a time into the coffee mixture then place on top of the vanilla ice cream, cutting biscuits as required. Spoon the coffee ice cream over the sponge finger layer. Smooth the surface. Dip the remaining biscuits one at a time into the coffee liquid and arrange over the coffee ice cream layer. Cover and freeze overnight.
Peel and slice the remaining mangoes. Lift the tiramisu from the tin, using the paper. Dust with cocoa. Slice and serve with fresh mango.