First, prepare the mushrooms. Brush off any dirt, then slice them. For medium sized mushrooms, I made three cuts, producing four slices.
Heat the butter and olive oil on low in a large flat lidded sauté pan. Add the garlic and stir for 30 seconds or so. Add the mushrooms and salt and immediately toss with two spatulas so everything is coated with oil. Cover the pan and cook the mushrooms for about 10 to 12 minutes, stirring occasionally and making sure the garlic doesn't burn. Reduce heat to very low, if necessary. During the cooking process, the mushrooms will release their moisture. Most of this will steam away as they cook; what remains will be garlicky and tasty. When the mushrooms are starting to turn golden, take the pan off the heat and set it aside for now.
In a Dutch oven or other lidded, heavy pot, heat enough olive oil to coat the bottom on medium-low, then add in the shallots, carrots, celery and garlic, and sauté for three or four minutes, until the shallots are translucent and the carrots are softening a bit. Then pour in the wild rice, stir, and add the mushroom stock, the bay leaf and tarragon, and the sautéed mushrooms and any liquid in their pan. Stir everything together and bring to a simmer.
Stir once, turn the heat down to low, cover with a tight-fitting lid, and let everything simmer gently for about 45 minutes. Check it occasionally and give it a little stir to make sure it isn't getting too thick or sticking to the bottom of the pot. If the soup is too thick, add more broth or water. This is done when the wild rice grains are just starting to burst—their mouth feel should be just a bit al dente.
Next, remove and discard the bay leaf. Stir in the spinach and cook for three or four more minutes (cook a little longer if using frozen spinach). Season with salt and pepper to taste. When serving, ladle the soup into individual bowls, then add a tablespoon or so of cream or half and half to each serving bowl. But honestly, this soup is soothing and delicious even without the cream. And it tastes great the next day too.