Preheat the oven to 390F (200C), with heat from up and down. Roll out the puff pastry into a thin circle, big enough to fit the bottom and sides of a 9 inch pie or tart pan. I ended up using a little more than 1/2 of my 15oz 400g block of puff pastry.
Lightly grease the pie pan, and press the puff pastry in it, pressing onto the bottom and going up to completely cover the sides of the pan. Prick the bottom with a fork (this will help keep it from bubbling up in the oven.) Place in fridge until ready to use.
Heat the butter in a large skillet over medium heat. Once melted, add the onion, and saute for a few minutes until starting to soften.
Add the crushed garlic and the pumpkin cubes, and cook for 7-8 minutes until pumpkin cubes are starting to soften. Add the baby spinach, and cook for another minute until wilted. Remove from heat and set aside.
In a large bowl, beat the eggs, then add in the heavy cream, feta cheese, salt, pepper, oregano, and nutmeg.
Add the cooked pumpkin mixture to this bowl, and mix to combine.
Pour the quiche batter into the prepared puff pastry crust until you fill the pan, you might have a little extra left over. Place pie pan on a baking sheet (to prevent any leaking) and bake on the middle rack of the oven.
Check on the quiche after 20 minutes, if the top is browning too quickly, cover loosely with foil. Keep baking for another 20-25 minutes or until a knife inserted in the center comes out clean. If you can, lift a little piece from the corner to make sure that the bottom pastry has cooked through.
Cool slightly and serve either at room temperature, or place in the fridge to serve cold!