Cook the wild rice. Rinse 1 cup of wild rice under cold water. Add it to a pot with 3 cups of water and a pinch of salt.
Bring to a boil, then simmer, covered, for 40–50 minutes until tender and slightly chewy. Drain any excess water and set aside.
Sauté the vegetables. In a large pot or Dutch oven, heat 1–2 tablespoons of olive oil over medium heat. Add onion, carrots, and celery with a pinch of salt.
Cook 6–8 minutes until softened. Stir in garlic and cook 30 seconds until fragrant.
Build the broth. Add the chicken broth, bay leaf, thyme, and rosemary if using. Bring to a gentle simmer.
Let it bubble for 10 minutes to marry the flavors.
Make the roux. In a separate small saucepan, melt 4 tablespoons of butter over medium heat. Whisk in 1/3 cup flour and cook 2–3 minutes, stirring, until it smells nutty and looks golden. Slowly whisk in 2 cups of milk or half-and-half until smooth and thickened, 3–4 minutes.
Combine and thicken. Pour the creamy roux into the soup pot while stirring.
Simmer 3–5 minutes to thicken slightly.
Add the chicken and rice. Stir in the cooked wild rice and shredded chicken. Simmer another 5 minutes. If it’s too thick, add a splash of broth or milk.
Season with salt and plenty of black pepper.
Finish and serve. Remove the bay leaf. Add a small squeeze of lemon for brightness, if you like. Ladle into bowls and garnish with chopped parsley.
Serve with crusty bread or a simple salad.