Grease a large crockpot.
Cut chicken breasts into 2-3 even pieces (to cook evenly).
Rinse the rice to remove excess starch and add to the crockpot.
Add diced onion and cut carrots and mushrooms (and celery if desired)
Add in the minced garlic, poultry seasoning, dried parsley, bay leaves and pepper to taste
Pour 3 cups of chicken broth over everything and stir.
Cover and cook on high for 2 1/2 - 4 1/2 hours or until the chicken is cooked through, rice is tender, and most of the liquid has been absorbed.
Near the end of the crock pot cooking time, melt the butter in a small pot over medium heat.
Slowly add in the flour, whisking constantly, and the whisk the mixture for an additional 1 minute.
Then whisk in the remaining 1 cup chicken broth very slowly.
Allow the mixture to thicken.
Then very slowly whisk in the whole milk and allow to thicken.
Shred the chicken in the crockpot and then add the cream mixture and cheddar cheese.
Stir and mix well.