Heat butter in a large skillet over medium heat. Once it melts, add in onion, celery and carrots. Cook 2 - 3 minutes or until they start to soften. Add in garlic, thyme and sage. Cook an additional 30 seconds to 1 minute or until garlic is fragrant.
Sprinkle flour over the top. Mix well and cook for 1 minute.
Slowly whisk in chicken broth. Bring to a boil and then reduce heat and simmer. Add 1 tablespoon of hot broth to the cream to temper it then slowly whisk cream into the broth. Cook until broth thickens slightly.
Stir in chicken and rice. Season to taste with salt and pepper.
Transfer to a casserole dish and top with buttery crackers. Bake in 350 degree oven for 20 - 25 minutes or until the edges are bubbly and the top has browned. Garnish with a sprinkle of fresh thyme leaves, if desired.
Notes
For texture purposes, it is best if the rice is on the cooler side. Day old rice is even better! If you want to make this casserole ahead, I would make it to the point of putting it in the casserole dish. Top with the crackers just before baking. This ensures that the crackers stay crunchy. Nutrition information for estimation purposes only.