In a large bowl, dissolve yeast in warm water. Add the milk, sugar, shortening, eggs, salt and 3-1/2 cups flour; beat until smooth. Stir in enough remaining flour to form a soft dough.
Turn onto a floured surface; knead until smooth and elastic, about 6-8 minutes. Place in a greased bowl, turning once to grease top. Cover and let rise in a warm place until doubled, about 1 hour.
Meanwhile, in a large skillet, cook bacon over medium heat until crisp. Using a slotted spoon, remove to paper towels. In a Dutch oven, cook the beef, onion, salt and pepper over medium heat until meat is no longer pink; drain. Add bacon and cheese; cook and stir until cheese is melted. Remove from the heat.
Punch dough down. Turn onto a lightly floured surface; divide into fourths. Roll each portion into an 12-in. x 8-in. rectangle; cut each into six squares. Place 1/4 cup meat mixture in the center of each square. Bring corners together in the center and pinch to seal.
Place 2 in. apart on greased baking sheets. Bake at 400° for 9-11 minutes or until lightly browned. Brush with butter. Serve warm with ketchup if desired. Yield: 2 dozen.