In a large skillet, melt the butter over medium heat. Add the pears and the thyme and cook until the pears are tender and any juice has evaporated, 4 to 6 minutes. Season to taste with salt and pepper. Transfer to a plate to cool completely.
Working with 1 sheet of puff pastry at a time, on a lightly floured surface, roll the dough out to a 10-by-15-inch rectangle. Trim about 1/8 inch off of each edge. Cut the dough into 6 equal squares. Transfer the squares to a parchment-lined baking sheet. Repeat with the remaining dough.
Brush a 1-inch border of egg on each square. Divide the cheese among the 12 squares. Then divide the pear mixture among the squares. Fold the squares over into triangles and press to seal with a fork. Transfer the pies to the freezer for 15 minutes.
Preheat the oven to 400 degrees F.
Brush the tops and sides of the pies with the egg. Cut a slit in each pie to allow steam to escape. Bake the pies until deep golden brown and puffed, 20 to 25 minutes, rotating halfway through. Transfer to a rack to cool slightly and serve warm.
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