Prepare the grill for direct cooking over medium heat (180°C to 230°C).
Place the asparagus and scallions in a large bowl and turn to coat them with the oil. Brush the cooking grates clean. Grill the asparagus and spring onions over direct medium heat, with the lid closed, until marked by the grill but not dark, 4 to 6 minutes, turning once or twice. Transfer the vegetables to a cutting board. Coarsely chop them and place in a medium saucepan.
Place the asparagus and scallions in a large bowl and turn to coat them with the oil. Brush the cooking grates clean. Grill the asparagus and spring onions over medium heat, with the lid closed, until marked by the grill but not dark, 4 to 6 minutes, turning once or twice. Transfer the vegetables to a cutting board. Coarsely chop them and place in a medium saucepan.