Add 1 tablespoon oil and 1/4 teaspoon salt, tossing well to coat.
Place asparagus on grill rack coated with cooking spray; grill 4 minutes or until crisp-tender, turning after 2 minutes.
Combine remaining 1/4 teaspoon salt, vinegar, and next 3 ingredients (through garlic); stir with a whisk. Slowly pour remaining 2 tablespoons oil into vinegar mixture, stirring constantly with a whisk. Stir in capers. Arrange asparagus on a serving platter; drizzle with vinaigrette, and sprinkle with basil.