Rinse wild rice in a fine-mesh strainer under cold water 30 seconds.
Melt butter with olive oil in a Dutch oven; saute onion, carrots, celery 6-7 min until soft.
Add mushrooms, cook 5 min; add garlic, thyme, rosemary, cook 1 min.
Sprinkle flour over vegetables, stir 2 min to make roux.
Whisk in 2 cups broth to dissolve roux, then add remaining 6 cups broth, rice, bay leaves, salt, pepper.
Bring to gentle boil, reduce heat, cover, simmer 40-45 min until rice splits and curls.
Nestle chicken breasts into simmering soup for last 20 min until cooked through.
Remove chicken, shred with two forks, return to pot; discard bay leaves.
Reduce heat to lowest, stir in heavy cream, warm 3-4 min (do not boil).
Season to taste, ladle into warm bowls, top with parsley, serve with crusty bread.
