Grate the zest of one lime into a medium bowl. Peel and finely grate the horseradish into the same bowl, then add the lime juice (about 3 tbsp) and the sesame oil. Stir to combine and set the dressing aside.

Chop the avocados into small pieces and place them in a medium bowl. Finely chop the cucumber and add it to the bowl. Chop a good handful of dill, removing the thick stems, and add it to the bowl, using as much as you like. Add 2 to 3 tbsp of lime juice and gently toss everything together.

Lay a slice of smoked salmon on a smooth work surface and trim it into a rough rectangle. If the slice is uneven or not long enough, add a piece of extra salmon with a slight overlap. The rectangle should measure roughly 5 × 16 cm, but it does not need to be exact.

Place a heaping tablespoon of the avocado mixture about 5 cm from one short end of the salmon. Fold the short end over the filling and begin rolling it up. The mixture may fall out and look messy at first, but once a tube begins to form, stand the roll upright and continue rolling until complete. Return any fallen avocado mixture to the top of the roll, tidying it as needed, and add more filling if the roll is not full.

Use a small spatula to slide under the roll and place it on a small serving plate. Add a few fingerfuls of arugula to the plate as a garnish.

Whisk the dressing with a fork until creamy, then fold in the capers. If the dressing is too thick, add a little more sesame oil or lime juice to taste. Drizzle the dressing over the arugula and lightly over the salmon roll, sprinkle with black sesame seeds, and serve.