In a small saucepan, simmer the water and sugar over medium heat until sugar dissolves, or about 5 minutes.
Remove from heat, then stir in the coffee liqueur.
Pour the simple syrup into a jar and chill in the fridge until ready to use.
Brush the simple syrup onto the cooled cakes, then wrap them up in plastic wrap and freeze until ready to assemble.
For the chocolate espresso mousse
In a large bowl, combine the melted chocolate, espresso powder, salt, egg, egg yolk, and vanilla. Use an electric hand mixer to blend until smooth.
In a small saucepan, bring the water to a boil.
Add the boiling water to the chocolate mixture and mix until smooth.
In the same saucepan, bring 227g (1 cup) heavy cream to a simmer (190 F), then add to the mixture and blend until smooth.
In a separate medium bowl, add the remaining 170g (¾ cup) heavy cream and use an electric mixer to beat until stiff peaks form.
Add the whipped cream to the chocolate mixture and gently fold with a rubber spatula until fully combined.
Place in the fridge for at least one hour to set.