Melt butter in large kettle, add onions and saute until transparent but not browned. Add beef broth and chicken stock base. Cover and simmer 2 to 3 hours. Remove from heat and refrigerate overnight or several hours. Discard chilled surface fat. Reheat and season to taste with white pepper. Slice cheese into 12 slices. Lightly toast 12 bread slices and top each with 1 slice Jack cheese. Pour soup into individual ovenproof serving bowls and top with slice of bread and cheese. Run bowls under broiler just until cheese bubbles and is soft but not browned.
