Preheat oven to 375.
Butter a 13x9 baking dish and set aside.
Heat olive oil in a dutch oven over medium heat.
Add onions and butternut squash.
Season with salt and pepper and add thyme.
Lower heat to medium-low, cover and cook, stirring occasionally, for 15 to 20 minutes, or until squash is tender.
Remove lid and discard thyme sprigs.
Stir in spinach and continue to cook for 3 minutes.
In the meantime combine beaten eggs, nutmeg and feta cheese in a mixing bowl.
Remove squash mixture from heat and taste for salt and pepper; adjust accordingly and let stand 5 minutes.
Stir in egg mixture; set aside.
Unfold phyllo sheets.
Place a phyllo sheet in the bottom of the prepared baking dish.
Brush with melted butter.
Top with nine more sheets, brushing each sheet with melted butter before adding the next.
As you work, keep the unused stack of phyllo sheets covered so they don't dry up.
Spread squash and spinach mixture over phyllo in dish.
Top with remaining 10 phyllo sheets, brushing each sheet with melted butter, including the top sheet.
Bake for 35 to 40 minutes, or until top is browned and flaky.
Let stand 10 minutes.
Cut and serve.