Sauté the vegetables: In a large pot, melt the butter over medium heat. Add the diced onion, carrots, and celery. Sauté for about 5 minutes, until the vegetables start to soften.
Add garlic and seasonings: Stir in the minced garlic, thyme, parsley, salt, and black pepper. Cook for another 30 seconds until fragrant.
Pour in broth and chicken: Add the chicken broth and shredded chicken. Bring the mixture to a gentle boil, then reduce heat to low and let simmer for 10 minutes.
Cook the noodles: Add the egg noodles and continue simmering for 8–10 minutes until they are tender.
Make it creamy: In a small bowl, whisk together the milk, heavy cream, and flour until smooth. Slowly pour the mixture into the soup while stirring continuously. Simmer for 5 minutes, allowing the soup to thicken.
Enhance the flavor: Stir in the Parmesan cheese and lemon juice, if using. Adjust seasoning to taste.
Serve and enjoy: Ladle the creamy chicken noodle soup into bowls, garnish with fresh parsley, and serve warm.