Arrange a rack at the bottom of the oven and heat to 450 degrees. With the stalk end facing up, slice the cauliflower in half through the stalk, then when your knife reaches florets, pull the pieces apart. (Pulling instead of cutting through the florets will prevent little buds from falling off.) Continue to slice through the stalks and pull apart florets until pieces are no thicker than 1 inch.

In a large bowl, toss the cauliflower pieces with the olive oil; season with salt and pepper. Spread in an even layer, cut sides down, on a parchment-paper-lined pan. Roast, undisturbed, on the bottom rack until golden brown on the underside, 15 to 20 minutes. (Check pieces in the middle of the pan, because pieces at the edges brown faster.)

Flip the cauliflower, sprinkle with the Parmesan, then roast until the cauliflower is tender and the Parmesan is melted and golden in spots, 7 to 10 minutes. Let cool a few minutes for the Parmesan to crisp. Use a spatula to transfer the cauliflower and any cheese on the sheet pan to plates.