Prepare 250 ml of espresso coffee and let it cool completely.
Melt the butter in a double boiler or in a microwave on low and let it cool.
Grease an 21×21 cm (8×8 inch) glass (or similar size) or ceramic baking dish with butter. Line the bottom and sides with parchment paper so it sticks well.
Preheat your oven to 150 °C (about 300 °F) static mode.
Separate the egg whites from the yolks in 2 mixing bowls.
With an electric mixer, whisk the egg yolks with the sugar until the mixture is pale and fluffy.
Pour in the melted butter, continuing to whisk, then gradually add the sifted flour, stirring with a spatula until you get a smooth batter.
Mix in the cold coffee and milk, using a whisk to blend everything into a thin, liquid mixture.
In another bowl, whip the egg whites until they form stiff peaks.
Gently fold the beaten egg whites into the egg yolk mixture, using slow, upward motions to keep them fluffy. Pour the batter into the prepared baking dish.
Bake in your preheated static oven at 150 °C (about 300 °F) for approximately 80 minutes, until the top is golden. If it browns too quickly, cover it with foil.
Once baked, let the cake cool completely at room temperature. Then, cover it with plastic wrap and refrigerate for at least 2 hours to set.
Once set, remove the cake from the dish, discarding the parchment paper. Cut into cubes using a smooth, wet knife or nylon thread for clean edges.
Dust with powdered sugar before serving this unique three-layered coffee cake!