Melt butter in a large heavy Dutch oven over medium-high heat. Add sliced cremini and shiitake mushrooms and cook undisturbed for 4-5 minutes until caramelized and golden on the edges.
Add diced onion, carrots, celery, and minced garlic to the pot. Sauté for 4-5 minutes until the vegetables begin to soften and become fragrant.
Sprinkle all-purpose flour over the vegetables and stir continuously for 2 minutes to cook the roux and coat the ingredients evenly.
Gradually pour in vegetable broth while stirring to deglaze the pot and dissolve the roux. Stir in wild rice blend, fresh thyme, rosemary, salt, and black pepper.
Bring soup to a simmer, then reduce heat to low, cover with a tight-fitting lid, and cook for 40-45 minutes until the wild rice grains are tender and curled.
Uncover and stir in heavy cream. Simmer gently for another 3-5 minutes until rich and velvety.
Remove from heat, taste and adjust seasoning with additional sea salt and black pepper as needed, ladle into warm bowls, and serve with artisan sourdough bread!