Transfer the olive oil and the mushrooms to a pot and sauté over high heat until they water out, then continue sautéing them stirring frequently until all the juices evaporate and mushrooms are well browned and fragrant (this can take from 10 to 20 minutes).
Reduce heat to medium, add the onion, salt, pepper, and thyme, and stir until onion is soft, about 3-4 minutes.
Bring to a boil, and reduce heat to a gentle simmer. Cook covered for 20-30 minutes or until the potato is fork tender.
Taste, adjust salt and pepper and return soup to the pot.