Place the asparagus on a rimmed baking sheet and drizzle tablespoons of the olive oil over. Toss gently to coat evenly. Sprinkle on the salt, and toss again. Roast for 7-10 minutes for thin stalks, 9-14 for thick ones. Remember that they will continue to cook a bit after you remove them from the oven, so take them out while they’re still a little firmer than you would like. The wide time ranges are because some people like their asparagus pretty crisp, some pretty soft.
Meanwhile, heat the remaining tablespoon of oil in a medium skillet over medium-high heat. Add the shallots and sauté for about 10 minutes until they are browned and just a bit crisp (not burned! Crisp).
During the past minute of roasting the asparagus, pull out the baking sheet, scatter the Parmesan over the spears and return to the oven so that the Parmesan melts slightly.
Transfer the asparagus to a serving platter, and scatter the shallots over the top. Season with pepper, and if you like, squeeze the lemon over all or some of the asparagus. Serve hot or warm.