Holding both ends of each asparagus spear, break them where they naturally want to snap. Discard the stems. Toss the snapped asparagus with some olive oil and a generous pinch of salt. Lay the asparagus neatly on a sheet tray and roast until the asparagus is pliable and starting to turn brown, 13 to 15 minutes. Set aside.
Toss the arugula with the lemon zest and juice, 1 tablespoon olive oil and a pinch of salt in a bowl. Taste to make sure it is delicious. Lay the arugula on a serving platter. Top with the roasted asparagus, hazelnuts and Parmigiano.