Do I need parchment paper?
It makes your life easier, yes. Parchment helps prevent sticking and makes cleanup basically a victory lap. A silicone baking mat also works well. Foil is risky because the cheese can fuse to it.
Why did my crisps turn out chewy instead of crispy?
Usually one of three things: (1) they needed another 1 to 2 minutes in the oven, (2) they were made too thick in the center, or (3) they got stored before fully cooled. Bake until the edges are deep golden and the bubbling slows down, then let them cool on the pan so they finish crisping.
Can I use pre-shredded Parmesan?
You can, but results vary. Pre-shredded often has anti-caking agents and thicker shreds, which can melt less evenly. For the crispiest, laciest edges, use finely grated Parmesan (the fluffy snow from a microplane or the small holes on a box grater).
If you mean the shelf-stable grated Parmesan in the green can, it will work in a pinch, but it tends to melt a little drier and less lacy. Still crunchy, just different.
What cheese works besides Parmesan?
Hard, aged cheeses are your friends: Pecorino Romano, Asiago, or a Parmesan-Pecorino mix. Higher-moisture, young cheeses often spread into greasier puddles and stay more flexible (not wrong, just a different vibe).
How do I make them into shapes for bowls or garnishes?
Bake as usual, then while they are still warm and pliable, drape over a rolling pin for a taco shape, or press into a small inverted bowl. Work fast, they set in about a minute.