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Step 1
Preheat oven to 450F.
Step 2
On a clean and lightly floured surface, prepare and roll out the puff pastry into a 10x15-inch rectangle. Transfer to a large half sheet baking pan lined with parchment paper.
Step 3
Use a knife to gently score a 1-inch border around the pastry dough. Make sure to score the pastry with shallow cuts and do not cut through the pastry.
Step 4
Use a fork to lightly poke holes all over the pastry dough (inside the scored border). Do not poke through the dough. This allows the steam to escape during baking so that the pastry doesn't puff up in the oven.
Step 5
Sprinkle Gruyère cheese evenly over the pastry inside the border and top with asparagus in a single layer alternating ends and tips.
Step 6
In a small bowl, add olive oil, balsamic vinegar, salt, and pepper, and stir well to combine. Brush the mixture evenly over the asparagus and top with Parmesan cheese.
Step 7
In another small bowl, whisk together egg and milk. Brush the egg wash over the border on all sides.
Step 8
Bake for 15 to 20 minutes until the crust is golden brown and puffy. Let the tart cool for 2-3 minutes before slicing and serving.