In a Dutch oven or soup pot, over medium-high heat, melt the butter. Add the chopped vegetables: onion, celery, and potatoes. Saute the vegetables for 5-7 minutes until the onions are translucent. Stir in the minced garlic and thyme sprigs. Once the garlic is fragrant (about 1 minute), add the shredded chicken and broth.
Bring the soup to a boil, then reduce to a lively simmer and cover the pot. Cook the soup for 20-25 minutes, until the chopped potatoes are soft and the thyme leaves fall from the stem.
Add the zucchini and carrot noodles to the soup. Place the cover on the pot and allow the noodles to simmer in the soup until al dente (about 6-7 minutes).
Season the soup with salt and pepper. I use 2 teaspoons of salt since my homemade broth doesn't contain any salt. The broth used will determine the amount of salt you need. I recommend starting with 1 teaspoon and adding more salt as needed. Remove the thyme stems before serving.