Grill bell pepper for 10 minutes over medium, turning often to char all sides.
Seal pepper in a plastic bag to steam for 10 minutes.
Slit pepper and drain juice into a blender.
Peel and seed the pepper, then chop.
Add chopped pepper to the blender with cloves, 2 Tbsp oil, vinegar, basil, salt and pepper. Puree until very smooth.
Toss asparagus with remaining oil in a bowl to coat.
Grill for 8 minutes, turning occasionally.
Return the asparagus to the bowl.
Pour the vinaigrette over the asparagus and toss to coat well.