Cook wild rice blend according to package directions.
Set aside.Melt 1 tablespoon butter in a large pot over medium heat.
Sauté onion, carrots, and celery for 4 minutes.
Add garlic and cook 30 seconds more.Add chicken broth and all four herbs. Season with salt and pepper. Increase heat to medium-high, add chicken breasts, and bring to a boil.
Cover, reduce to medium-low, and simmer 12–16 minutes until chicken is cooked through, flipping once if breasts are thick.Remove chicken and shred into bite-sized pieces on a cutting board.
Keep soup warm over low heat.In a separate saucepan, melt remaining 6 tablespoons butter over medium heat.
Whisk in flour and cook 1½ minutes.
Slowly whisk in milk, then heavy cream.
Stir constantly until thickened.Add cream mixture, shredded chicken, cooked rice, and lemon zest to the soup pot.
Stir to combine and remove from heat.Taste, adjust seasoning, and serve hot.