Preheat your oven to 400°F (200°C). Roll out the thawed puff pastry and press it into a 9-inch tart pan or pie dish, trimming any excess edges. Prick the bottom with a fork.

Melt the butter in a large skillet over medium heat. Add the sliced leeks and cook for about 10-12 minutes until softened and tender, but not browned. Stir in the fresh thyme, salt, and pepper.

Remove the leeks from the heat and let them cool slightly for 5 minutes so they don't scramble the eggs later.

In a medium bowl, whisk together the eggs, heavy cream, and a pinch of nutmeg until smooth.

Spread the cooked leeks evenly over the bottom of the prepared pastry crust. Scatter the cubes of Brie cheese on top of the leeks.

Pour the egg and cream mixture carefully over the leeks and cheese, ensuring it fills the gaps.

Bake for 30-35 minutes, or until the pastry is golden brown and the filling is set and slightly puffy.

Let the tart cool for 10 minutes before slicing to allow the custard to firm up. Serve warm.