Preheat oven to 450 F and line a baking sheet with parchment paper.
Bring a large pot of water to a boil and prep a colander and an ice bath. Once the water starts to boil, carefully add the broccoli and allow them to cook in the water for 2-3 minutes. Immediately remove from heat and drain the broccoli in the colander, then transfer them to the ice bath to prevent further cooking.
Form small mounds of cheese on your baking sheet (note: my process photos show the mounds all touching, this will prevent the chips from getting completely crisp, but is easier!). Transfer the broccoli to a cutting board, and use the bottom of a cup to smash it until it's thin. Place each floret on a mound of cheese. Repeat until you've used all the broccoli.
Sprinkle the broccoli side of your chips with salt and pepper. Bake in the preheated oven until the cheese has crisped, about 10 minutes.
Allow them to cool slightly on the counter, the cheese will harden and crisp as it cools. And enjoy!