Cook 1 tablespoon oil and garlic in 12-inch skillet over medium heat, stirring often, until garlic turns golden but not brown, about 3 minutes.
Add tomatoes and olives and cook until tomatoes begin to break down, about 3 minutes; transfer to bowl.
Heat remaining 1 tablespoon oil in now-empty skillet over medium-high heat until shimmering.
Add half of asparagus with tips pointed in 1 direction and remaining asparagus with tips pointed in opposite direction.
Shake skillet gently to help distribute spears evenly (they will not quite fit in single layer).
Add 1 teaspoon water, cover, and cook until asparagus is bright green and still crisp, about 5 minutes.
Uncover, increase heat to high, and cook, moving spears around with tongs as needed, until asparagus is well browned on 1 side and tip of paring knife inserted at base of largest spear meets little resistance, 5 to 7 minutes.
Season with salt and pepper to taste.
Transfer asparagus to serving platter, top with tomato mixture, and sprinkle with basil and Parmesan.
Serve.