To prepare the potatoes for ribbons, carefully slice ⅛-inch thick slices along the length of the potatoes to achieve thin, uniform slices. The longer the slices of the potato, the more ribbons like the final result will be. Submerge the potato slices in cold water for 30 minutes to remove excess starch.

To prepare the herb butter, combine butter and olive oil in a small saucepan and heat until the butter starts to foam. Add the chopped garlic, rosemary, lemon zest, and a couple cracks of black pepper. Turn off the heat and set the pan aside to cool.

To assemble the potato ribbons, strain the potatoes from the water and thoroughly dry them with a towel. Place the potatoes into a large bowl, add the herb butter, and generously massage all the potato slices. Season liberally with salt and pepper.

Set the oven to 375°F. Oil a shallow 9-inch, oven-proof saucepan or cast iron pan and roughly lay the potato slices in, pressing them down to create a compact layer inside the pan. The parchment's ridges will serve as a structural base to prevent the potato slices from falling over during cooking, and to give the dish a whimsical final result.

Mound the potato slices into the pan, keeping the edges vertical and folding the potato strips, accordion-style, leaning them against one another and against the pan. It will take a bit of time to arrange them, but keep folding and tucking the potato strips into the pan until it is tightly packed. You can cut and bunch bits of the parchment to fill in holes as necessary. Drizzle any excess herb butter over the top of the potatoes.

Bake the potato ribbons at 375°F for 20 minutes. Reduce the oven temperature to 350°F, top the potato ribbons with cheddar cheese, and keep baking them for an additional 30-35 minutes, until the top is golden brown and crispy.

Serve immediately, cutting along the natural folds of the roasted potato.