In a large pot, heat the olive oil over medium heat. Add the diced onion and sauté for about 3 minutes until translucent. Stir in the minced garlic and cook for an additional minute until fragrant.
Add the sliced carrots and celery to the pot, cooking for about 5 minutes until they start to soften.
Pour in the chicken broth and bring to a boil. Stir in the dried thyme, dried parsley, black pepper, and salt.
Once boiling, add the egg noodles and cook according to package instructions, usually about 7-8 minutes, until al dente.
Reduce the heat to low and stir in the shredded chicken, cream cheese, and cheddar cheese. Cook until the cheeses are melted and the soup is creamy, about 5 minutes.
Taste and adjust seasoning if necessary. Serve hot, garnished with chopped green onions.