Dissolve yeast in warm water in a mixing bowl.

Let the mixture sit for 5-10 minutes to activate the yeast.

Add warm milk, sugar, shortening, egg, salt, and 2 cups of flour to the yeast mixture.

Stir in the remaining flour until a soft dough forms.

Turn the dough onto a floured surface and knead for about 5 minutes until smooth and elastic.

Place the dough in a greased bowl, turning to coat all sides.

Cover the bowl with plastic wrap and then a towel.

Let the dough rise in a warm place for about 1 hour, or until it has doubled in size.

While the dough is rising, cook the ground beef and onion in a skillet until the beef is browned.

Drain off any excess grease.

Stir in the tomato sauce and set aside.

Once the dough has doubled, punch it down to release the air.

Divide the dough into 16 equal pieces.

On a floured surface, roll each piece of dough into a 5-inch circle.

Place 2 pieces of cheese on each circle, followed by 3 tablespoons of the beef mixture.

Fold the dough over to form a half-circle, and pinch the edges together to seal.

Place the stuffed buns on a greased baking sheet.

Cover the buns and let them rise in a warm place for about 30 minutes.

Preheat oven to 400°F (200°C).

Bake the stuffed buns for 8-12 minutes, or until they are golden brown.