Melt butter in a medium saucepan. Add mushrooms and green pepper; cook for 5 minutes. Blend in flour, salt, and pepper. Continue stirring and cooking until smooth and bubbly. Gradually add milk and chicken broth, stirring constantly. Cook for 10 minutes, stirring frequently. If you'd like a thicker sauce, blend 2 tablespoons of cornstarch with 1/4 cup cold water; add to sauce, a little at a time, until desired thickness is reached. Cook for a few more minutes. Add chicken and pimiento; heat through. Serve on toast points or pastry shells or rice. Chicken a la King Recipe serves 6 to 8.