Preheat oven to 400 degrees.
Open your thawed puff pastry and place it on a parchment lined sheet pan.
Pinch the edges of the pastry to form a little "dam." Set aside.
Trim any tough, woody ends of the asparagus.
Lightly steam the asparagus (I do it in a plastic bag in the microwave for about a minute. Just add trimmed asparagus and about 2 Tablespoons water)
Add ice to your "steaming" bag or hold steamed asparagus in a bowl of ice. You just want to keep the bright green color and stop the cooking process.
Add the butter and cream to a large skillet.
Simmer over low heat until the cream reduces by 1/3 to 1/2 begins thickening.
Whisk in the garlic, salt, and pepper for one minute.
Whisk in the parmesan cheese until melted.
Spread the thickened alfredo sauce generously over the pastry.
Arrange the asparagus on the sauced pastry and bake for 20 to 30 minutes, until golden brown. Remove from the oven and allow to set and cool for 3 - 5 minutes.
Cut into wedges or squares and serve.