In a large saucepan, melt butter over medium heat.
Add dried beef that has been cut into chunks or broken into little pieces.
Brown chipped beef in butter for 2 to 3 minutes; add flour.
Stir flour and beef together; the beef should clump up. Cook, stirring constantly for 1 minute.
Gradually add milk (about a cup at a time) while slowly stirring.
Bring milk mixture to a slow boil until a thick gravy forms, approximately 8 to 10 minutes.
Add salt, pepper, and Worcestershire sauce and stir to incorporate before serving.
Serve it over lightly toasted bread that has been lightly buttered.