Preheat the oven to 180ºC and prepare a removable round mold, about 20-22 cm in diameter. Cover the bottom with parchment paper and grease the sides with butter or oil. Melt the butter and reserve.
Sift the flour with the cocoa powder and salt two or three times, to avoid lumps. Arrange the eggs with the sugar in a bowl and beat with a wire mixer until double or triple its size. Add the flour with the cocoa and mix with rods, by hand. Add the butter and vanilla, and mix gently.
Fill the mold, carefully break the bubbles on the surface using a spatula and bake for about 20-25 minutes, until it comes out clean when punctured in the center with a toothpick. Wait 10 minutes out of the oven, unmold and turn upside down on a wire rack to cool.
Drain the possible liquid from the cream cheese and beat with a few rods in a bowl. Add the sifted icing sugar and beat until incorporated. When the cake is cold, arrange a round layer on top without leading to the edges. Use a spatula to smooth it out. Mix the rest of the cheese with black food coloring and draw the face of Jack Skellington with a pastry bag.