Bring a large pot of salted water to a boil and add 1 cup of wild rice to the pot. Turn the heat to simmer and let the wild rice cook for about 45 minutes or until it begins to crack and curl. When the rice is done, strain the water from the rice and set aside.
While the rice is cooking, heat a large pot or Dutch oven over medium/high heat and add olive oil. Once the olive oil is fragrant add the onion to the pot and sauté for 2-3 minutes. Add the chopped mushrooms and a pinch of salt, toss and allow the mushrooms to cook off some liquid for about 5 minutes.
Next, add the garlic, butternut squash, carrots, and celery, to the pot and season with the remaining salt and pepper. Cook for about 4-5 minutes to allow the squash to caramelize a bit with all the other vegetables.
Tie the thyme and rosemary together with cooking twine and place the bundle into the pot and pour the broth, Worcestershire, and one cup of whole milk over the vegetables and stir. Bring the soup to a gentle boil. Add the turkey to the pot, reduce the heat and allow the soup to simmer for about 5 minutes.
Heat a separate small saucepan over medium heat and add the butter to the saucepan. When the butter is melted add the flour and whisk the two together. Let the mixture cook for 1 minute and then pour the remaining 1 cup of milk into the pan. Whisk until all the ingredients are combined and the mixture is a thick roux.
Scrape the roux into the large pot with all the other ingredients. Whisk all of the ingredients together until there are no lumps. Add the peas and cooked rice to the pot, mix, and allow the mixture to simmer for 5-10 minutes or until it begins to thicken.
Remove the pot from the heat and remove the herb bundle. Let the soup rest for 10-15 minutes. The longer the soup rests, the thicker it will get. If you want a thicker consistency, let it rest longer. If you want a thinner consistency, eat the soup right away or add more broth.