Preheat oven to 325 degrees. Butter a 2 quart oval baking dish.
With an electric beat eggs and sugar on medium- high speed until very thick and pale yellow, approximately 5 to 10 minutes.
Add vanilla, cocoa powder, and flour. Mix until just combined. With the mixer on low, slowly pour in butter and mix until combined.
Pour 1/2 the batter into the prepared baking dish. Add peanut butter cups, then top with remaining batter. Drizzle the melted peanut butter. Swirl with a knife or a toothpick.
Place baking dish in a larger baking pan. Add hot tap water to the pan to come halfway up the side of the baking dish. Bake for 50 minutes to 1 hour. Although very hard, allow to cool slightly before digging in, serve warm or at room temperature with a scoop of ice cream!