Preheat the oven to 350 F.
Butter a 9 inch pring form pan and cover the bottom with parchment paper.
Next, break up the chocolate into chunks and melt it with the milk in a double boiler, about 10 minutes.
While the chocolate is melting, cut the room temperature butter into one inch chunks.
When the mixture is smooth and the chocolate is completely melted, remove it from the heat.
Pour the chocolate into a mixing bowl. On low speed add alternate tablespoons of butter and egg yolk until thoroughly mixed, 5 minutes.
Make sure the batter is completely smooth before stopping the mixer and scraping down the sides.
Pour the batter into the prepared springform and place it in the oven. You may want to put a tray under the springform because the butter might leak.
Bake 25 minutes. Remove from the oven while the cake is still jiggly.
Allow to cool at room temperature before putting in the fridge.