Finely chop the chives. Crush the pink pepper berries in a mortar and pestle.
In a bowl, whisk together the balsamic vinegar, olive oil, salt, pepper, honey, chives, and both mustards.
Arrange the lamb's lettuce on a platter or plate. Cut the mozzarella into thick slices and arrange on top. Halve the figs and distribute them on the salad.
Drizzle the vinaigrette over everything and let it sit at room temperature for 10–15 minutes before serving.