Beat the eggs with the sugar and vanilla for 2 minutes on a high speed mixer. Add the butter and cocoa and beat for a minute.
Add the baking powder and flour. Beat not long at all. The dough is dense, with a spoon does not flow. Put the dough in a form (22 cm) and send it to the oven at 180 g for 40 minutes. Use a dry wooden skewer.
When the pie is almost ready, make the filling. Add condensed milk to the milk and put it on the stove. Do not boil, bring to 70 degrees, stirring the filling. Get the pie out of the oven, make punctures with a skewer all over the pie. Fill the hot pie with milk filling. Allow the pie to cool completely, place on a platter and sprinkle with powdered sugar if desired.