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1
In a large skillet, melt the butter and oil over medium-high heat.
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2
Stir in the shallot and cook, stirring often, until fragrant, 40 to 60 seconds.
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3
Add the mushrooms and keep cooking, stirring constantly, until the moisture from the mushrooms evaporates and begins to brown, about 4 minutes.
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4
Continue cooking, stirring often, until almost all of the moisture evaporates and the mushrooms color to a dark brown, about 9 minutes.
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5
Remove the pan from the heat and pour in the wine.
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6
Return the skillet to the heat and stir, scraping any flavoring from the bottom of the pan, until the wine is absorbed, about 3 minutes.
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7
Remove from heat, stir in the thyme and season with salt and black pepper to taste.
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8
Set the mushroom mixture aside and let cool, then stir in the grated cheese.
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9
Roll the puff pastry into a rectangle measuring 20 by 10 inches, the dough will be just over 18 inch thick.
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10
Divide the dough into 8 (5-inch) squares.
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11
Then arrange the squares on 2 parchment-lined baking sheets.
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12
Let chill for about 20 minutes.
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13
Meanwhile, divide the filling into 8 equal portions:
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14
Gently press some of the filling into a 13 measuring cup.
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15
Unmold the filling and, press the filling with your hand into an oval bal.
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16
Repeat with the remaining filling, and you should be able to use all of the filling.
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17
Set aside.
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18
Brush the beaten egg along 2 of the 4 edges of each square.
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19
To assemble the turnover, place one mound of filling in the center of each square.
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20
Working quickly, pick up a square and fold it in half diagonally and press gently, sealing the edges together.
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21
Keep forming the remaining turnovers, then check each turnover again to make sure the seal holds.
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22
Brush the remaining beaten egg over each of the turnovers, and prick the top of each with a knife to form vent holes.
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23
Chill the turnovers on the baking sheets for about 20 minutes before baking.
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24
Meanwhile, place the oven rack in the center, and preheat the oven to 425F (220C).
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25
Bake the turnovers 1 sheet at a time, until puffed and golden brown, 25 to 35 minutes, rotating the sheet halfway through.
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26
Let cool for a few minutes enough to handle.
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27
Serve warm or at room temperature.
