01 - Preheat oven to 400°F. Line a 9-inch tart pan with parchment paper.
02 - Roll out the puff pastry and press it into the prepared tart pan. Trim excess pastry and prick the base with a fork. Chill in the refrigerator while preparing the 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 sliced mushrooms to the skillet and continue cooking for 8 to 10 minutes until mushrooms release moisture and turn golden. Stir in minced garlic and thyme leaves, cook for 1 additional minute. Remove from heat and allow to cool slightly.
05 - In a mixing bowl, whisk together eggs, heavy cream, salt, and black pepper. Fold in grated cheese until combined.
06 - Evenly spread the onion and mushroom mixture over the chilled pastry shell. Pour the egg and cheese custard evenly on top.
07 - Bake in the preheated oven for 25 to 30 minutes, or until the filling is set and the pastry is golden brown.
08 - Let the tart cool for 10 minutes before garnishing with fresh herbs. Slice and serve warm or at room temperature.