1. Preheat the Oven:

• Preheat your oven to 400°F (200°C).

2. Prepare the Pastry:

• Roll out the puff pastry on a lightly floured surface.
• Cut the pastry into circles using a cookie cutter or a glass.
• Place the pastry circles on a baking sheet lined with parchment paper.
• Score a smaller circle inside each pastry circle, being careful not to cut all the way through.

3. Cook the Mushrooms and Shallots:

• Heat the olive oil and butter in a skillet over medium heat.
• Add the mushrooms, shallots, and garlic. Sauté until the mushrooms are tender and the shallots are translucent.
• Add the fresh thyme leaves and season with salt and pepper. Cook for another 2 minutes.

4. Assemble the Tarts:

• Spread a layer of goat cheese inside the scored circle of each pastry round.
• Top with the mushroom and shallot mixture.
• Drizzle a little heavy cream over the mushroom mixture.

5. Bake:

• Brush the edges of the pastry with the beaten egg.
• Bake in the preheated oven for 15-20 minutes, or until the pastry is golden brown and puffed.

6. Serve:

• Garnish with fresh thyme sprigs.
• Serve warm.