Place dried porcini in a small bowl and cover with 1 cup hot broth. Let soak 20 minutes until softened. Lift out mushrooms, chop roughly, and reserve soaking liquid. Strain the liquid through a fine-mesh sieve lined with a paper towel to remove grit.

Melt 2 tablespoons butter in a large Dutch oven over medium-high heat. Add cremini and shiitake in a single layer. Cook undisturbed 4-5 minutes until browned on the bottom, then stir and cook 3 minutes more until deeply golden and reduced by half. Transfer to a bowl.

Reduce heat to medium. Add remaining 2 tablespoons butter, onion, and celery. Cook 6-7 minutes, stirring occasionally, until softened and just starting to color. Add garlic, thyme, and chopped porcini. Cook 1 minute until fragrant.

Add wild rice, 5 cups broth, reserved porcini soaking liquid, and soy sauce. Bring to a boil, then reduce heat to low, cover, and simmer 45-50 minutes until rice is tender and split open. Stir occasionally and add remaining 1 cup broth if soup gets too thick.

Stir in the sautéed mushrooms and any accumulated juices. Simmer uncovered 5 minutes. Remove from heat and stir in heavy cream. Season with salt and pepper to taste. The soup should be creamy but still brothy, with distinct grains of rice.

Ladle into bowls and top with fresh parsley. Serve with crusty bread.