01 - Preheat oven to 400°F. Line a 9-inch tart pan with parchment paper.
02 - Roll out puff pastry and press into the prepared tart pan. Trim excess and prick base with a fork. Chill in refrigerator while preparing filling.
03 - Heat olive oil and butter in a large skillet over medium heat. Add sliced onions and cook, stirring occasionally, until soft and golden, about 12 minutes.
04 - Add mushrooms to skillet and cook for 8 to 10 minutes until moisture evaporates and mushrooms turn golden. Stir in minced garlic and thyme; cook another minute. Remove from heat and let cool slightly.
05 - In a bowl, whisk eggs, heavy cream, salt, and pepper. Fold in grated cheese until combined.
06 - Evenly spread the onion and mushroom mixture over chilled pastry. Pour egg and cheese mixture on top.
07 - Bake for 25 to 30 minutes until filling is set and pastry is golden brown.
08 - Allow tart to cool for 10 minutes before garnishing with fresh chives or parsley. Serve warm or at room temperature.