In a large pot, heat the olive oil or butter over medium heat. Add the chicken and season with salt and pepper. Cook until browned and cooked through, about 6-8 minutes per side. Remove the chicken from the pot and set aside.
In the same pot, add the minced garlic and sauté for about 30 seconds until fragrant. Sprinkle in the flour and stir continuously for about 1 minute to cook off the raw flavor.
Gradually whisk in the chicken broth, ensuring there are no lumps from the flour. Bring the mixture to a gentle simmer.
Add the egg noodles, dried thyme, and dried parsley to the pot. Cook according to package instructions until the noodles are tender, usually about 6-8 minutes.
While the noodles are cooking, shred the chicken into bite-sized pieces. Once the noodles are ready, return the shredded chicken to the pot.
Stir in the milk or half-and-half and heavy cream. Allow the soup to simmer for an additional 3-5 minutes, letting the flavors meld together.
Taste and adjust seasoning with salt and pepper as needed. Serve hot, garnished with fresh parsley.