Add the chicken breasts and chicken broth to the pot. Bring to a boil, then reduce heat and simmer until the chicken is cooked through, about 15 minutes. Remove the chicken, shred it, and set aside.
Stir in the heavy cream, shredded cheddar, and softened cream cheese to the pot, keeping the heat low and simmering until the cheeses melt and the soup becomes creamy.
Add the egg noodles, dried parsley, dried thyme, salt, and pepper to the pot. Simmer until the noodles are tender, about 10 minutes.
Return the shredded chicken to the pot, add the crumbled bacon, and stir to combine. Heat through for a minute or two, adjusting seasoning if needed.
Ladle the soup hot into bowls and garnish with chopped green onions or chives.
Notes
For a lighter version, you can substitute half and half for heavy cream and reduce the amount of cheddar cheese.