1. Cook the egg noodles in a large pot of salted boiling water until just al dente, then drain and set aside.

2. In a large deep skillet, melt the butter with the olive oil over medium heat.

3. Add the onion, carrots, and celery and sauté until the vegetables are softened and starting to turn golden, about 6 to 8 minutes.

4. Stir in the garlic, salt, pepper, thyme, and poultry seasoning and cook until fragrant, about 1 minute.

5. Sprinkle the flour over the vegetables and cook, stirring constantly, for 1 to 2 minutes to remove the raw flour taste.

6. Slowly whisk in the chicken broth, followed by the milk and heavy cream, stirring until the sauce is smooth and beginning to thicken.

7. Fold in the shredded chicken, peas, and chopped parsley and simmer for 3 to 5 minutes, until everything is hot and the sauce has a rich, creamy consistency.

8. Add the cooked egg noodles to the skillet and toss gently to coat them in the sauce, adding a splash of broth or milk if you prefer a looser sauce.

9. Stir in the lemon juice and Parmesan if using, adjust seasoning to taste, and serve hot with extra parsley on top.