Melt butter in a large skillet over medium-low heat; add onions and green peppers. Cook, stirring, until onions are tender. Remove to a warm platter and keep warm.
In a mixing bowl, combine ground beef, bread crumbs, egg, 1/2 teaspoon salt, and 1/4 teaspoon pepper. Mix gently with hands or fork. Shape mixture into four 1/2-inch thick oval patties.
Over medium-high heat, brown the steaks quickly on both sides; reduce heat to medium-low, cover, and continue cooking for 15 to 20 minutes longer, or until cooked through.
Combine the flour, water, ketchup, and sherry; blend well. Pour the ketchup mixture over the Salisbury steaks; add the cooked onions and peppers. Cover and simmer until the sauce is thickened.
Calories per serving: 379