Combine the chicken stock and yogurt in a medium saucepan on medium heat. Whisk until combined. The yogurt and stock won’t completely emulsify until it has simmered for a while.
Meanwhile, melt the butter in a pan on medium heat. Once it is bubbling, add the garlic and cook for a minute, stirring often. Add the mushrooms, chives, and salt and pepper (to taste) and sauté for 3 to 5 minutes, until the mushrooms are creamy. Add 1/4 cup fish sauce and cook for another 1 to 2 minutes.
Add the spiralized parsnips and toss, cooking for a minute or so. Add to the saucepan with the chicken stock and yogurt along with the carrots and shredded chicken. Simmer until the carrots are tender, about 5 to 7 minutes. Season to taste with fish sauce, salt, and pepper.