Preheat oven to 475°F. Line a baking sheet with parchment paper.
In a medium bowl (or directly on the parchment-lined baking sheet), toss broccoli stalks with olive oil, salt, and pepper, making sure that the broccoli is thoroughly coated and the oil and seasonings are evenly distributed. Spread broccoli slices out evenly on the baking sheet, making sure the slices aren't piled on top of each other.
Bake for about 13 minutes, until the broccoli has developed some roasted brown spots.
Remove broccoli from oven, stir and flip the broccoli, and then spread the broccoli back out on the baking sheet. Evenly top each broccoli slice with some of the cheese.
Return broccoli to oven and bake for about 2 minutes more, just until the cheese is melted and a little browned and bubbly.
Broccoli stalks: To yield 2 cups of slices, you will need about 4-7 stalks, depending on how thick the stalks are and how far up each stalk you use.
Peeling the stalks: We use a vegetable peeler to quickly and easily remove the tough outer layer of the stalks. The stalks tend to be tougher at the bottom and require little or no peeling as you get toward the top, where the florets were. We don't recommend putting the peels down your garbage disposal.
Parmesan Cheese: To make this pasta recipe truly vegetarian, be sure to select a parmesan cheese made with non-traditional enzyme alternatives from microbes or fermentation, rather than the traditional rennet.
Make-ahead step: You can peel the broccoli stalks and slice the "chips" earlier in the day or even a day ahead. Wrap the slices tightly (so they don't dry out) and store them in the fridge until you're ready to finish the recipe.