Step 1: Prepare the Filling

1. Heat butter and olive oil in a large skillet over medium heat.
2. Add the sliced shallots and sauté for 3–4 minutes until softened and translucent.
3. Stir in the garlic and cook for 1 minute until fragrant.
4. Add the mushrooms, thyme, salt, and pepper. Cook for 8–10 minutes, stirring occasionally, until the mushrooms are tender and browned.
5. Pour in the white wine or vegetable stock and cook for an additional 2 minutes, allowing the liquid to reduce. Remove from heat and let cool slightly.

Step 2: Prepare the Puff Pastry

1. Preheat your oven to 200°C (180°C fan) or 400°F. Line a baking sheet with parchment paper.
2. Unroll the puff pastry sheet and cut it into 6 equal rectangles or circles, depending on your preference.
3. Score a 1 cm (1/2 inch) border around the edge of each piece with a knife, being careful not to cut all the way through.

Step 3: Assemble the Tarts

1. Spread a thin layer of softened goat cheese onto the center of each pastry, staying within the scored border.
2. Spoon the mushroom mixture evenly over the goat cheese.
3. Brush the edges of the pastry with the egg wash for a golden finish.

Step 4: Bake the Tarts

1. Bake in the preheated oven for 20–25 minutes, or until the puff pastry is golden and puffed.

Step 5: Garnish and Serve

1. Remove the tarts from the oven and let them cool slightly.
2. Garnish with fresh thyme leaves or parsley, if desired, and serve warm.