Cook wild rice according to package directions, about 40 minutes in boiling water. Drain and set aside.
Heat up a large dutch oven pot over medium high heat and add in 1 tablespoon olive oil. Add the garlic, onion, celery, and carrot and saute for 2-3 minutes.
Add in the sliced mushrooms and top with vegetable broth. Cover with a lid and bring to a simmer, about 10 minutes. Add in the salt, pepper, and dried herbs. Stir and give it a taste.
Add in the wild rice to the soup and reduce the heat to low.
In a small sauce pot, melt the butter over medium heat.
Add in the flour and stir with a wooden spoon until the paste becomes light brown. Use a whisk to whisk in the whole milk and half-and-half until a thick mixture forms, about 4-5 minutes.
Transfer the roux mixture from the pot and whisk it into the soup, bringing it back to a gentle simmer for 2-3 minutes. Once the soup is creamy and homogeneous, turn off the heat. (If the soup is too thick, add a touch of water; similarly if it's too thin, just let it simmer a little while longer).
Serve immediately and garnish with chopped chives.