Add 1 tablespoon of the butter to a large pot or Dutch oven over high heat. Allow the butter to melt.
Add the chicken breasts, and sear for a few minutes on each side, to add color and flavor to the chicken. It doesn’t need to be cooked all the way through at this point.
Remove the chicken breasts and set aside.
Deglaze the pot with the white wine, cooking for a few minutes at high heat until the flavor from the chicken is removed from the pan. (optional)
Add one more tablespoon of the butter to the same pot that you cooked the chicken in.
Add the chopped carrots, onions and potatoes and sauté for 10 minutes over medium heat, stirring occasionally.
Add the remaining 4 tablespoons butter and the flour to a small saucepan.
Cook over medium heat for 3-4 minutes, stirring constantly. Add 1 cup of the chicken broth and cook for an additional 3 minutes, stirring occasionally.
Dice the seared chicken breasts into small cubes, approximately 1/2” in size.
Add the roux, diced chicken, remaining chicken broth, cream, minced garlic, salt and pepper to the pot with the vegetables.
Bring to a simmer and cover for 30 minutes, or until the carrots and potatoes are tender and the chicken is cooked through.
A few minutes before serving, add the chopped kale to the soup.
Allow it to simmer for two minutes.