Sprinkle the flour on the work surface. Unfold the pastry sheet on the work surface. Roll the pastry sheet into a 10-inch square. Cut into 4 (5-inch) squares.
Heat the oil in a 10-inch skillet over medium heat. Add the onion and cook until tender, stirring occasionally. Remove the onion from the skillet.
Increase the heat to medium-high. Add the sandwich steaks to the skillet and cook for 3 minutes or until cooked through, stirring occasionally.
Spoon one-fourth of the onion and one-fourth of the sandwich steaks on the bottom third of each pastry square. Top each with 1 slice cheese. Fold 2 opposite sides over the filling. Roll up like a jelly roll. Brush the pastries with the egg. Place the pastries onto a baking sheet.
Bake for 20 minutes or until the pastries are golden brown. Let the pastries cool on the baking sheet on a wire rack for 10 minutes. Cut the pastries in half diagonally to serve.