Cook egg noodles according to package directions. Drain and set aside.

In a large pot over medium heat, melt the butter. Add the onion and cook until translucent. Add garlic and cook for 1 minute.

Remove from heat and stir in flour. Add salt and pepper. Gradually add chicken broth and milk, stirring constantly until smooth. Return to heat and bring to a boil, stirring continuously.

Add cooked noodles, peas and carrots, cooked chicken, and rosemary. Cook until heated through.

Serve hot, garnished with chopped fresh parsley if desired.