Preheat the oven to 400 degrees. Snap off woody ends of the asparagus.
On a baking sheet, toss the asparagus with 1 tablespoon olive oil, sea salt and pepper until evenly coated. Spread the asparagus in a single layer.
Roast until tender-crisp and lightly-browned, about 12-15 minutes. Roast time is dependent on the thickness of the asparagus.
Add basil, lemon juice, lemon zest and olive oil to a food processor or blender and pulse until roughly minced. Remove asparagus from oven and toss with basil sauce. Sprinkle with flaky sea salt and serve immediately.