Heat olive oil in a large pot over medium heat. Add onion, garlic, carrots, and celery. Sauté for about 5 minutes until softened.
Add chicken breasts and chicken broth. Bring to a boil, then reduce heat and simmer for about 15 minutes until chicken is fully cooked.
Remove chicken from the pot, shred it with two forks, and set aside.
Stir heavy cream, cheddar cheese, and cream cheese into the pot. Cook over low heat until melted and smooth.
Add egg noodles, parsley, thyme, salt, and pepper. Simmer for 8–10 minutes until noodles are tender.
Return shredded chicken to the pot and stir in crumbled bacon. Taste and adjust seasoning as needed.
Ladle soup into bowls and garnish with green onions or chives. Serve hot.