Start the mushrooms first. Heat olive oil over medium-low. Add mushrooms, oregano, and a pinch of salt and pepper. Stir once to distribute, then cook 10-15 minutes, stirring two or three times in the process. The mushrooms will release their juices. If they begin to char too much or an aggressive simmering noise heaves from your stovetop, turn the heat down a touch. Towards the end of the cook time, pour in apple cider and heat until the liquid is absorbed by the mushrooms, about 5-8 minutes. Remove from heat and cover.
As the mushrooms, cook, heat 2 tbsp olive oil in a large stockpot or Dutch oven over a medium setting. Add onion, carrot, and celery and cook until soft and fragrant, about 3-5 minutes. Toss in garlic and stir for about 1 minute.
Pour wild rice, stock or broth, and a pinch of salt and pepper into your pot. Bring to a boil, then low to a simmer and cook with the lid cracked off the edge of the pot, stirring occasionally, for 25-30 minutes. The rice will absorb much of the liquid and soften. If the water creeps too low for your liking, add another 1/2-1 cup to ensure the rice doesn't burn to the bottom of the pot.
Once rice is tender, pour in milk and toscana and mix until cheese melts and soup thickens and is creamy. Remove from heat and add spinach, stirring gently until it wilts.
To serve, ladle soup into bowls and top with a small handful of mushrooms. Garnish with parsley, if you'd like.