Rinse 1 cup of wild rice blend under cold water. In a medium saucepan, combine the rinsed rice with 4 cups of water. Bring to a boil, then reduce heat to a simmer, cover, and cook for 45-50 minutes until the rice is tender and has burst open. Drain any excess water.
While the rice cooks, melt 2 tablespoons of unsalted butter in a large Dutch oven or heavy-bottomed pot over medium-high heat. Add the sliced mushrooms and cook for 8-10 minutes, stirring occasionally, until they have released their liquid and turned golden brown. Transfer the mushrooms to a bowl and set aside.
In the same pot, melt the remaining 4 tablespoons of butter. Add the finely chopped onion, diced carrots, and diced celery. Cook for 6-8 minutes, stirring frequently, until the vegetables have softened.
Add the minced garlic and cook for 1 minute until fragrant. Sprinkle the 1/3 cup of flour over the vegetables and stir constantly for 2 minutes to form a pasty roux.
Slowly pour in the 6 cups of broth, whisking constantly to prevent lumps. Add the fresh thyme and bay leaf. Bring the soup to a simmer and cook for 10 minutes, stirring occasionally, until the broth has slightly thickened.
Stir in the cooked wild rice, reserved mushrooms, 1 cup of heavy cream, and 2 tablespoons of dry sherry. Simmer for 5 more minutes until heated through. Season generously with kosher salt and freshly ground black pepper to taste. Remove the bay leaf before serving.