Add the broth, ham, chicken, onion, carrots, garlic, salt, pepper, and tarragon to the slow cooker. Cook on low for 4 to 5 hours or high for 2 ½ to 3 hours. Heat milk on the stovetop then whisk in cheese until melted. Using a fork, mix together the softened butter and flour. Add both the milk mixture and butter mixture and whisk into soup until it is creamy and well combined.