Preheat a grill to medium-high (about 400–450°F). Clean the grates.
Rinse the asparagus, pat dry, and snap or trim off the woody ends (about 1–2 inches). If spears are very thick, peel the lower third with a vegetable peeler.
In a large bowl, toss the asparagus with the extra-virgin olive oil, kosher salt, and black pepper until evenly coated.
Arrange the asparagus perpendicular to the grates (or use a grill basket). Grill, covered, turning once or twice, 5–8 minutes (8–10 minutes for thick spears), until the stalks are tender-crisp and lightly charred in spots.
Transfer to a platter, rest 1 minute, and taste for seasoning. Serve with lemon wedges for squeezing at the table.