In a large pot, heat the butter over medium-high heat. Add the onion, carrots, and celery. Cook until vegetables are tender about 5 minutes. Add the garlic and cook for 2 more minutes.

In a small bowl, whisk together the milk and flour. Pour the mixture into the soup pot and stir, making sure there are no lumps of flour. Stir in the chicken broth. Add the shredded chicken and thyme. Season with salt and pepper.

Bring the soup to a low boil and stir in the egg noodles. Cook for 10 minutes, stirring occasionally, or until noodles are soft. Stir in the heavy cream, lemon juice, and parsley. Taste and add additional salt and pepper, if necessary.

Ladle the soup into bowls and serve warm.