In a large pot, melt the butter over medium heat. Add the onion and garlic, sautéing until translucent and fragrant, about 5 minutes.

Sprinkle the flour over the sautéed onions and garlic, stirring constantly to cook the flour, about 2 minutes.

Slowly pour in the chicken broth, stirring continuously to avoid lumps. Bring the mixture to a simmer.

Add the shredded chicken to the pot and let the soup simmer for about 20 minutes to blend the flavors.

Using an immersion blender, carefully blend the soup directly in the pot until smooth. Alternatively, transfer to a blender in batches.

Stir in the heavy cream and season with salt and pepper. Heat through.