Trim the hairy bottom of the white part of the leeks. Trim the dark greens, leaving the white and light green part only.
Cut the leeks in half lengthwise, then rinse them well (there’s often dirt trapped in there) and dry. Arrange them in a 9 X 13 baking dish, cut side down.
Drizzle the leeks with the olive oil and use your hands to thoroughly coat them. Sprinkle them with salt and pepper.
Roast them for 20 minutes. Remove from the oven, turn so that their cut side is up, sprinkle with the Parmesan, then continue roasting until fork-tender and golden brown, about 10 more minutes.
The baking times listed here are merely a suggestion. The idea is to cook the leeks until they are browned and caramelized. That's when they lose their sharpness and become wonderfully sweet and flavorful. So when you pull them out of the oven, if they're not golden brown, put them back in for a few more minutes, until they become caramelized.