In a heavy pot or dutch oven, melt 2 tablespoons of the butter over medium heat.
Add the chicken. Season with ½ teaspoon salt and ½ teaspoon of pepper and cook until just cooked through, about 5-6 minutes. Trasfer chicken to a plate and set aside.
Add the remaining 2 tablespoons of butter, carrots, celery and onion and cook for 3-4 minutes until the veggies become tender.
Add the garlic and flour and cook, stirring occasionally for 2 minutes.
Slowly whisk in the broth and add in the potatoes, fresh herbs, and the remaining salt and pepper. Simmer for 15-20 minutes until the potatoes are tender when poked with a fork.
Stir in the cream and reserved chicken and bring back to a simmer for a couple of minutes. Turn off the heat.
Ladle into bowls and garnish with fresh minced parsley.
Notes
Store leftovers in an airtight container in the fridge for up to 4-5 days. Reheat gently in a saucepan over medium-low heat.You can freeze this soup, but be careful not to overcook the potatoes. Defrost slowly in the refrigerator overnight, then reheat carefully so the potatoes don't fall apart and become mushy.