Remove hard part near the root end of asparagus and slice into about 2 inch length.
Wash sweet potato well and do not remove peel. Slice into about 1/4 inch round slices and soak in cold water for about 5 minutes. Drain well and blot dry with towel.
Add 2 tsp oil in a frying pan and when heated put in asparagus and sweet potato rounds. Turn down the heat to medium and grill until lightly colored and turn them to grill the other side. Turn the heat down to low and cover the pan for 3 more minutes.
Place dashi soup in a pot or sauce pan and add sweet potato rounds and asparagus. Cook for about 2 -3 minutes on medium heat. Add 3 T miso (white or combination white/red) and dilute the miso. When diluted, turn the heat off. Sprinkle in minced green onion.