Step 1: Preheat the oven

• Preheat your oven to 400°F (200°C).
• Line a baking sheet with parchment paper.

Step 2: Prepare the asparagus

• In a small bowl, mix the olive oil and minced garlic.
• Brush the asparagus spears with the garlic-infused olive oil mixture and season with salt and pepper.

Step 3: Prepare the puff pastry

• Roll out the thawed puff pastry sheet on a lightly floured surface into a 9-inch circle.
• Transfer the pastry to the prepared baking sheet.

Step 4: Assemble the tart

• Sprinkle half of the shredded Gruyere cheese evenly over the puff pastry, leaving a small border around the edges.
• Arrange the seasoned asparagus spears on top of the cheese, alternating the direction of the tips for a decorative effect.
• Sprinkle the remaining cheese over the asparagus.

Step 5: Bake the tart

• Brush the edges of the puff pastry with the beaten egg to create a golden crust.
• Bake the tart in the preheated oven for 25-30 minutes, or until the pastry is golden brown and the asparagus is tender.

Step 6: Serve 

• Remove the tart from the oven and let it cool for a few minutes before slicing.
• Garnish with fresh thyme leaves, if desired.