Cook egg noodles according to package directions, drain. Rinse with cold water, and drain again. Combine with next 6 ingredients; stir well. Add noodles and toss lightly; set aside.
Place each piece of chicken between 2 sheets of wax paper; flatten to 1/4 inch with meat mallet or rolling pin. Place a slice of cheese over each piece of chicken, and top with 1-2 tablespoons of noodle mixture. Fold long sides of chicken over noodles and cheese;fold ends over and secure with wooden picks. Spoon remaining noodle mixture into a lightly freased 12 x 8 x 2 inchbaking dish; set aside.
Dip chicken in egg, coat with bradcrumbs. Melt 1/3 cup butter in a heavy skillet; brown chicken on all sides. Place chicken over noodles in baking dish.
Dissolve bouillon cube in boilingg water. Saute onion and green pepper in 2 tablespoons butter until tender. Add flour; stir until smooth. cool 1 minute; stir constantly, until thickened. Stir in last 4 ingredients, pour over chicken. Bake uncovered at 400 F for 20-30 minutes.