Heat a griddle pan (or ordinary frying pan). Place the chicken breasts in the pan and cook for 8–10 minutes on each side. When cooked, remove from the pan and cut roughly into chunks.
Cut the red onions into wedges, keeping the root ends intact to hold the wedges together. Place in the pan and cook for 5 minutes on each side. Remove from the pan and set aside.
Place the flat pieces of red pepper in the pan and cook for 8 minutes on the skin side only, so that the skins are charred and blistered. Remove and set aside, then cook the asparagus in the pan for 6 minutes, turning frequently.
Put the boiled potatoes in a large bowl. Tear the basil, reserving a few leaves intact to garnish, and add to the bowl, together with the chicken and all the vegetables. Add the olive oil, balsamic vinegar and seasoning. Toss the salad and garnish with the reserved basil leaves.