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Preheat oven to 375 degrees F.
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In large bowl, toss butternut squash with 2 tablespoons olive oil, thyme, nutmeg, salt and pepper. Arrange on rimmed sheet pan in single layer; bake 25 minutes or until tender.
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Meanwhile, in large sauté pan over medium-high heat, combine 1 tablespoon olive oil and butter. Once glistening, cook onions 10 minutes, stirring occasionally.
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Reduce heat to medium; continue cooking onions 10 to 15 minutes, until soft and light brown.
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In large bowl, use fork to mash roasted butternut squash. Set squash and caramelized onions aside until cool enough to handle.
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Reduce oven temperature to 350 degrees F. Line sheet pan with parchment paper.
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On lightly floured surface, roll out puff pastry sheets. Cut each into 9 equal squares (18 total). Gently stretch each square to 4”x4”.
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In center of each puff pastry square, drop 1-1/2 tablespoons butternut squash, 1/2 tablespoon caramelized onion and 1/2 to 1 teaspoon feta cheese.
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Brush edges of pastry squares with egg wash; fold to form triangle. Use fork to crimp edges.
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On prepared sheet pan, arrange turnovers 1/2" apart. Brush top of pastries with remaining egg wash. Bake 20 to 25 minutes, until golden brown. Serve warm.