Heat the olive oil in a large pot or dutch oven. Add the onion, carrots, celery, and garlic and saute until the carrots start to soften, about 5 minutes. Add the seasonings and zest and cook another 2 - 3 minutes.
Stir in the wild rice and vegetable broth and bring the soup to a boil. Cover and reduce to simmer, cooking until rice has cooked, about 30 - 40 minutes.
Once the rice is cooked and soft, stir in the milk, lemon juice, and spinach. Stir until spinach is wilted.
Serve immediately and enjoy! Soup can be frozen and reheated as desired.