Start by shredding your cooked chicken into bite-sized pieces. Slice the carrots and celery, chop the onion, and mince the garlic. Having everything prepped before you start cooking makes the process smooth and fast.
Heat the olive oil in a large pot over medium heat. Add the chopped onion and cook until translucent, about 3-4 minutes. Then add the minced garlic, sliced carrots, and celery. Sauté for another 5 minutes until the vegetables start to soften and release their aromas.
Pour in the chicken broth and stir in the dried thyme. Season with salt and pepper, but keep the salt moderate as you can adjust later. Bring the mixture to a gentle boil.
Once boiling, add the egg noodles to the pot. Cook according to package instructions, usually about 6-8 minutes, until the noodles are tender but still have a slight bite. Stir occasionally to prevent the noodles from sticking.
Add the shredded chicken to the pot. Let everything simmer together for 5 more minutes so the flavors meld and the chicken heats through. Taste and adjust seasoning with more salt and pepper if needed.
Ladle the chicken and noodles into bowls and serve hot. This dish is perfect on its own or paired with a simple side salad or crusty bread.