In large mixing bowl dissolve yeast in warm water. Add milk, sugar, shortening, eggs, salt and 3-1/2 cups of flour. Beat until smooth. Stir in enough of the remaining flour to form a soft dough.
Turn onto a floured surface, knead until smooth and elastic, 6-8 minutes. Place in a greased bowl turning once to coat the top. Cover and let rise until doubled in size, about 1 hour.
Meanwhile in a large skillet cook bacon until crisp and drain on papertowels. In a dutch oven cook hamburger meat. Drain. Add onion and salt and pepper and cook until onion is soft. Add bacon and cheese and stir until cheese is melted.
Heat oven to 400 degrees. Punch dough down. Divide into fourths. Roll each portion to 12 x 8 rectangle. Cut each rectangle into 6 squares. Place 1/4 cup of meat mixture on each square and bring up corners to meet and twist to seal. This will leave an open slit on each corner. Bake in oven until golden brown. Brush with melted butter and serve warm.