In a large pot, melt 2 tablespoons of butter.Add carrots, onions and celery and sauté until tender.Add in chicken broth and fresh parsley.Bring to a boil.Add in noodles and cook until noodles are tender, about 7-8 minutes.Remove from heat.In a saucepan over medium heat melt butter.Stir in flour and whisk constantly for about 1½ - 2 minutes.Slowly pour in milk, whisking constantly.Stir in heavy cream and bring to a light boil.Boil lightly until sauce thickens, continue stirring.Pour sauce into chicken noodle soup and stir until combined.Add in cooked diced chicken.Season with salt and pepper if needed.Serve immediately.Garnish with chopped fresh parsley.