Heat cooking oil in Dutch Oven over medium heat and add carrots, celery, and onions. Saute until tender. (Tip: carrots take longest to cook so I often add them in before I chop up the celery and onion)
Add garlic and cook for 1-2 minutes longer, or until garlic is fragrant.
Remove carrots, celery, onion, and garlic from the pot and set aside.
Turn the heat on low and add 1 stick of butter and let melt, then sprinkle in flour. Whisk the mixture to form a roux and continue cooking for 3-5 minutes to cook out any flour taste, continually whisking.
Slowly stir heavy cream into the roux, continuing to whisk.
Once the cream has been incorporated stir in chicken stock.
Add chicken, herbs, and seasonings to the soup and let simmer 30+ minutes while you make the dumplings.