In a large bowl, beat together the eggs and sugar until very thick; the batter should fall from the beaters in a thick ribbon. Beat in the vanilla.
While you’re beating the eggs and sugar, heat the hot chocolate and butter in a small saucepan to just simmering. Add the hot chocolate mixture to the egg mixture in a slow, steady stream as you continue beating.
In a separate bowl, whisk together the flour, baking powder, and salt. Fold the dry ingredients into the wet ingredients, stirring until they’re just combined.
Pour the batter into a lightly greased 9 inch cake round. Bake for 50 minutes, or until the cake is a deep golden brown and starting to pull away from the sides of the pan. Remove the cake from the oven and cool it in the pan for 10-15 minutes. Run a knife around the sides of the pan.