Rinse the wild rice under cold water for 30 seconds and set aside to drain. Slice the mushrooms ¼ inch thick and divide into two equal piles, then dice the onion, carrots, and celery and prep the remaining ingredients.
Heat the olive oil in a Dutch oven over medium-high heat. Add the first batch of mushrooms in a single layer, leave undisturbed for 2 minutes, then stir and cook 5 to 6 minutes until browned and dry. Season with ¼ teaspoon salt and transfer to a bowl.
Melt 1 tablespoon butter in the same pot, add the second batch of mushrooms, and repeat the browning process. Season with another ¼ teaspoon salt and transfer to the bowl, leaving the browned bits in the pot.
Reduce the heat to medium and add the remaining 2 tablespoons butter. Cook the onion, carrots, and celery for 6 to 8 minutes, scraping the bottom, then stir in the garlic and thyme and cook 30 to 60 seconds until fragrant.
Sprinkle the flour over the vegetables and stir constantly for 2 minutes. Pour in the sherry and scrape up the browned bits, cooking about 1 minute until the sherry has nearly evaporated.
Whisk in the broth about 1 cup at a time until smooth. Add the rinsed wild rice, bay leaf, browned mushrooms with their juices, remaining ½ teaspoon salt, and pepper, then bring to a boil and reduce to a low simmer with the lid ajar.
Simmer for 45 to 55 minutes, stirring every 10 minutes and scraping the bottom, until most grains have split open and curled. Add a splash of broth if the soup becomes too thick.
Discard the bay leaf and reduce the heat to low. Stir in the room-temperature cream and heat gently for about 5 minutes without boiling, then stir in the lemon juice and season to taste with salt and pepper.
Ladle the soup into warmed bowls, sprinkle each serving with chopped parsley, and serve right away.