In a heavy skillet, melt the butter over medium heat. Add the diced onion and sliced mushrooms to the skillet. Reduce the heat and cook, stirring occasionally, until the onions have become translucent and the mushrooms have softened, approximately 5 minutes.

Season the chicken strips with Greek seasoning and black pepper. Introduce the seasoned chicken to the skillet and continue to cook over medium heat, stirring regularly, until the chicken is evenly browned on all sides, about 5 minutes.

Concurrently, bring a large pot of lightly salted water to a boil. Add the egg noodles to the boiling water and cook them until they are tender yet firm to the bite, which typically takes about 10 minutes. Drain the noodles and set them aside.

Into the skillet with the chicken, pour the chicken broth, milk, and Worcestershire sauce. Gradually stir in the sour cream, adding one tablespoon at a time to prevent curdling. In a separate small bowl, whisk a small amount of the sauce with the flour until the mixture is smooth. Return this mixture to the skillet, stirring it into the rest of the sauce. Simmer the sauce until it has thickened, approximately 5 minutes.

Season the sauce with additional salt and black pepper to taste. Serve the chicken and sauce over the prepared egg noodles, garnished with chopped parsley.