Add the instant coffee to the milk, set aside. Cream the butter until light and fluffy, about 2 minutes. Beat in the vanilla. Gradually add the confectioner’s sugar, alternating with the milk until the icing is thick and smooth. Add the melted white chocolate and beat until smooth.
Unmold the cooled cakes onto a cardboard round. Cover the layer with about 1/4 of the icing. Place the second layer on top of the icing.
Use another 1/4 of the icing to do a crumb coat. This is a very thin layer of the icing that essentially traps the crumbs in place so that they are glued to the cake and won’t make a mess of the exterior of the cake. Freeze the cake for about 10 minutes to set the icing. Because of all the butter, it will harden quite quickly.
Now put about 1/3 of what is left of the icing on the top of the cake and spread it flat across the top. Put the rest of the icing on the sides of the cake. Don’t worry about what it looks like, just try to get it on as evenly as possible. You will smooth it out next.
Once the icing is on the cake hold the spatula straight up and down, at a slight angle away from the cake. Turn the cake turn table and hold the spatula steady, don’t press, just hold steady, and it will slowly scrape a thin layer off the sides and make them smooth. Once the sides are smooth then slide the spatula gently over the top of the cake to smooth it out, again you don’t want to apply too much pressure.