Preheat the oven to 450 F. Prepare the asparagus and then place on a baking sheet. Drizzle one tablespoon of the olive oil over the spears--and then roll them a little to ensure the oil is distributed evenly.
Roast for 10-15 minutes (depending on thickness of asparagus), until the spears are bright green, tender and charring in spots.
While the asparagus is roasting, heat the remaining two tablespoons of olive oil in a small skillet over medium heat. Add the garlic and cook until golden brown and fragrant, 1-2 minutes. Then add the lemon juice, zest, sesame seeds and parsley. Mix and heat through, a minute or two.
Transfer the cooked asparagus to a serving platter that is sloped or has sides (to keep the dressing from draining over the sides). Pour the prepared dressing over the asparagus. Sprinkle with flaked sea salt, toss and sprinkle one more time with flaked sea salt. Serve immediately.