Place the pastry dough on a lightly floured surface and roll it out to about 1/8 inch thickness with a rolling pin. Transfer the rolled dough to a parchment-lined baking sheet. Use a fork to pierce the crust evenly across the surface to prevent bubbling in the oven.
Trim the tough ends off the asparagus and halve the bunch lengthwise if desired. Spread the minced garlic over the prepared pastry crust. Arrange the asparagus spears evenly across the crust, leaving a small border around the edges.
1 sheet store-bought or homemade pastry dough
Brush the exposed edges of the pastry with olive oil using a pastry brush and sprinkle grated cheese evenly over the asparagus and crust. Season with salt and pepper to taste.
1 sheet store-bought or homemade pastry dough
Preheat the oven to 400°F (200°C). Bake the tart on the middle rack for 20-25 minutes or until the crust is golden brown and the cheese is bubbly. Lightly baste the asparagus with additional olive oil halfway through baking if desired.
Remove the tart from the oven and let it rest for 5 minutes. The asparagus should be tender with slightly roasted tips, and the crust crisp along the edges. Slice and serve warm or at room temperature.