None is the correct answer: Hugh Laurie did not win an Emmy for writing a House M.D. episode.
Laurie was nominated for Emmy Awards for his acting as Gregory House, but he did not receive an Emmy for writing the series. The show’s writing awards and nominations are associated with its writers and episodes, which can make this distinction easy to overlook.
“Three Stories” is one of House M.D.’s best-known episodes and won a Primetime Emmy Award for Outstanding Writing for a Drama Series for David Shore. “House’s Head” and “Wilson’s Heart” are important two-part episodes, but neither represents a writing Emmy won by Laurie.
This question separates acting credits from writing credits. Laurie was an executive producer and performed in every season, but those roles do not mean he authored the episode scripts. The answer is therefore a credit distinction rather than the title of an episode.