Prepare rice according to package directions.
While rice is cooking, in a large pot melt 4 TBS butter over medium heat.
Add in onion, carrot, and celery. Cook about 4-5 minutes until the onions start to get clear and they all start to get tender.
Add in minced garlic and cook for 1 minute.
Add in flour and cook for 1-2 minutes to fully coat the vegetables.
Slowly add in the chicken broth.
Add in thyme, marjoram, sage, rosemary, and salt and pepper.
Increase heat to medium high and bring to a boil.
Add chicken and cook for 12-15 minutes until chicken is cooked through.
Remove chicken breasts and set aside.
Reduce heat to medium low and add in cooked rice.
Shred chicken into bite sized pieces.
Add chicken back to the soup.
Add milk into the pot and whisk into the soup. Cook for about 5 minutes.
Stir in heavy cream and cook until soup reaches a desired consistency.