Preheat oven to 350°F.
Heat ¼ cup butter in saucepan until melted. Blend in flour, salt, and pepper. Cook over low heat, stirring constantly, until mixture is smooth and bubbly, remove from heat. Stir in water, milk, and bouillon cubes. Heat to boiling, stirring constantly. Boil and stir 1 minute; remove from heat. Stir in Worcestershire sauce and cheddar cheese until cheese is melted.
Cut peeled eggs lengthwise into halves. Arrange eggs in ungreased oblong baking dish (13 ½ x 9 x 2 inches). Sprinkle in vegetables. Pour cheese sauce over vegetables and eggs. Toss breadcrumbs with 2 tablespoons butter and the Parmesan cheese; sprinkle over top.
Bake uncovered in oven until mixture bubbles and crumbs are brown, 20 – 25 minutes. Garnish with parsley if desired. Serve over Texas Toast if desired.