Roll the puff pastry out to a thickness of about 1/8-inch, and cut into 8 equal squares.
Chill on a parchment-lined baking sheet.
Place the butter in a skillet and melt over medium heat.
Add the apples, brown sugar, flour, cinnamon, and salt, and saute until the apples are tender.
When the filling has cooled completely, spoon a small amount into the center of each puff pastry square.
Wet your finger with water and run it along 2 adjoining sides of the squares, then fold the squares over diagonally, forming triangles.
Press carefully to seal the edges, and use a sharp knife to cut vents in the top of each turnover.
Chill the turnovers in the refrigerator for 10 minutes.
Preheat the oven to 400 degrees F.
Bake the turnovers for 25 to 35 minutes, or until the pastry is golden brown and puffed.