01 - Preheat oven to 400°F. Line a 9-inch tart pan with parchment paper.
02 - Roll out puff pastry and press into the tart pan. Trim excess and prick base with a fork. Chill while preparing filling.
03 - Heat olive oil and butter in a skillet over medium heat. Cook onions, stirring, until soft and golden, about 12 minutes.
04 - Add mushrooms to the skillet and cook 8 to 10 minutes until they release moisture and turn golden. Stir in garlic and thyme; cook 1 minute more. Remove from heat and cool slightly.
05 - Whisk eggs, heavy cream, salt, and pepper in a bowl. Fold in grated cheese.
06 - Spread onion and mushroom mixture evenly over chilled pastry shell. 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. Garnish with fresh herbs if desired, slice, and serve warm or at room temperature.