Heat the olive oil in a large soup pot over a medium heat. Add the onions, celery and carrot and soften in the oil until fragrant and the onion is translucent, about 5 minutes. Add the garlic, mushrooms, bay leaves, and thyme and continue to sweat for a further 3 minutes.
Add the wild rice and the chicken breast. Pour the chicken broth into the pan and ensure that the chicken breast is covered. Top up with water if necessary. Bring the pot to a boil and turn the heat down to a simmer and cook for about 20 minutes, until the rice and chicken are cooked.
Once cooked, remove the chicken from the pot and use two forks to shred the chicken. Add it back to the pan and add the cream if you’re using it. Set aside while you make the roux sauce.
To make the roux sauce, melt the butter in a small sauce pan. Once it’s melted, add the flour and whisk to combine. Let the flour cook out for about 2 minutes. Slowly pour the milk into the pan while whisking to avoid lumps. Once all the milk has been added, bring the sauce to a boil. As soon as it has boiled it can be removed from the heat and added to the soup. Mix well. Add a squeeze of lemon juice and serve with fresh dill.