Put the seaweed in a medium bowl, cover plentifully with cold water and soak for 20 minutes, then drain and spin dry in a salad spinner. Meanwhile, thinly slice the tomatoes, season with a little salt in a bowl and set aside for 15 minutes. Whisk all the ingredients for the dressing together, with 2 tablespoons of water, in a medium bowl.
Combine the tomatoes and cucumber on a large plate and mix in the seaweed. Slice the avocado into long, fine strips in the skin, then use a dessertspoon to remove the slices in one go and arrange these in a pile in the middle of the salad. Drizzle over the dressing and scatter with chilli and sesame seeds.
It's best to eat this salad immediately, but if you're making for one, store leftover salad and dressing separately in the refrigerator for up to 2 days.