Preheat your oven to 400°F (200°C). Carefully unroll the thawed puff pastry sheet and press it into a 9-inch square or round tart pan. Prick the bottom all over with a fork and chill in the refrigerator for 10 minutes.
Line the chilled pastry with a piece of parchment paper and fill with pie weights. Blind bake for 15 minutes. Remove the parchment and weights, then bake for an additional 5 minutes until the crust is lightly golden. Reduce the oven temperature to 375°F (190°C).
In a medium mixing bowl, vigorously whisk together the eggs, heavy cream, chopped fresh herbs, kosher salt, and black pepper until completely smooth.
In a separate dish, toss the trimmed asparagus spears gently with the olive oil.
Scatter the crumbled goat cheese evenly across the bottom of the pre-baked pastry shell. Pour the egg custard mixture directly over the cheese.
Arrange the oiled asparagus spears in a single, even layer over the custard filling, trimming them to fit the tart pan if necessary.
Bake for 25 to 30 minutes, or until the egg custard filling is fully set and the edges of the pastry are a deep golden brown.
Remove the tart from the oven and let it cool for 10 to 15 minutes before slicing. Serve warm or at room temperature.