For the dressing, combine the garlic, lemon juice, olive oil, oregano, basil, sugar, salt and pepper in a jar with a lid. Shake to mix the dressing. Set to the side.
To prepare the asparagus, cut off the tip. Cut the tips in half. Holding the bottom of the asparagus with two hands, break the spear. Discard tough smaller end. With a vegetable peeler, peel long ribbons off the stalk. You won’t be able to peel the entire spear. With the thicker part, cut diagonally into thin strips.
Add the parsley and toss with the dressing. Place on platter. Sprinkle with the feta cheese and garnish with the olives.