Prepare the hot milk sponge cake. Cut the cake into two layers, and then cut each layer into pieces, so that you have pieces to fit your serving dish. You will need cake for three layers. You may have some leftover cake to save for another use.
In a small saucepan, simmer together the espresso powder, sugar, and water. Set it aside.
In a bowl, stir together the mascarpone, powdered sugar, and vanilla. Stir in the chocolate shavings. Set aside.
In the bottom of your 10x7 pan, place the first layer of your cake. Brush it all over with the espresso mixture. Spread this with a third of the mascarpone mixture. Repeat this with two more layers.
In the bowl of an electric mixer, beat the cream until it's well whipped. Beat in the vanilla and sugar. Spread this all over the top of the tiramisu and add then sprinkle on the chocolate shavings. Serve right away or chill for later.