Prepare the Onions and the Squash:

1. Preheat the oven to 400ºF and set racks in the lower and middle parts of the oven.
2. On a rimmed baking sheet, toss together the butternut squash, 1 tablespoon of olive oil, and a big pinch of salt. Roast in the preheated oven on the middle rack for 30 minutes, tossing halfway through, until the squash is tender with some caramelized bits. Remove and let cool to room temperature.
3. Meanwhile, In a wide, heavy-bottomed pan, heat the remaining 2 tablespoons of oil on medium heat. Add the onions and cook for 10 minutes, stirring a few times to make sure all of the onions get contact with the pan and start to soften.
4. Add a pinch of salt and stir to combine. Lower the heat to medium-low and let the onions sit undisturbed for 20 minutes.
5. Continue to cook for 15 more minutes, stirring the onions every 5 minutes at this point, a total of 3 times.
6. Stir in the balsamic vinegar and cook for about 5 more minutes. This is the point where the onions have the optimum texture and taste.
7. If you’d like your onions to be completely reduced and jammy, cook, stirring often, for another 10-15 minutes, but this is optional! Set aside to cool.

Prepare the Pastry:

1. Roll out the pie dough to an 11-inch circle. Fit the pastry into a 9-inch pie plate, making sure to press the pastry into the sides and the bottom. Crimp the edges as desired. Prick the bottom of the dough all over with a fork. Place the pie shell in the freezer for 15 minutes.
2. Increase the oven temperature to 425ºF.
3. Once chilled, line the pie shell with a round piece of parchment paper, then add pie weights (I recommend dry rice or beans or lentils), making sure to push the pie weights to the edges.
4. Bake on the lower rack for 20 minutes, then remove from the oven and carefully remove the parchment and pie weights. Return to the oven and bake for an additional 5 minutes. Set aside until ready to use.

Assemble and Bake:

1. Lower the oven temperature to 375ºF.
2. In a large bowl, whisk together the eggs, milk, cream, apple cider vinegar, salt, and pepper. Mix in the roasted squash, 1 cup of the caramelized onions, feta cheese, green onions, and thyme. Pour the filling into the parbaked crust. 
3. Bake on the middle rack for 35-40 minutes or until the filling is completely set. Transfer to a wire rack to cool. Let the pie cool for at least 5-10 minutes before slicing. 
4. Serve warm or at room temperature.