Preheat the oven to 400°F. Line two baking sheets with parchment paper.
In a small saucepan set over medium-low heat, melt the butter then add the onions, rosemary, and pepper and cook, stirring occasionally, until the onions are caramelized, about 20 minutes. Remove the caramelized onions from the heat and set them aside to cool slightly.
Lightly flour your work surface then unfold each of the puff pastry sheets. Cut each sheet into nine squares for a total of 18 squares.
Divide the caramelized onions and sliced fruit evenly among the squares, placing the fillings in the center of each square, then divide the cheese on top.
Brush around the edges of each turnover, then fold each square over to form triangles. Using a fork, crimp together the edges to seal each turnover shut.
Brush the tops of the turnovers with the remaining egg wash.
Using a paring knife, cut three small slits atop each turnover then transfer them to the baking sheets, spacing them at least 2 inches apart.
Bake the turnovers until the pastry is golden brown and puffed, 10 to 15 minutes.
Remove the turnovers from the oven and let them cool slightly before serving.
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