Poach the Chicken or use store bought rotisserie chicken: Poach the chicken or pull about 2-3 cups meat off the rotisserie chicken; shred the chicken.
In a large pot, warm olive oil + butter over medium heat. Add the bay leaf, chopped onions, carrots, celery, leeks, fennel and minced garlic. Saute until the vegetables are softened and translucent.
Add the flour over the veggies and mix very well. Pour in the chicken broth and add dried thyme. Season with salt and pepper to taste. Bring the mixture to a boil, then reduce the heat to simmer. Let it simmer for about 10-12 minutes to allow the flavors to meld.
Add the milk, parmesan cheese and cooked chicken to the pot. Simmer for an additional 5-7 minutes until the vegetables are tender, but still have a slight bite to them. Taste and adjust if needed.