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