Soft-boil the eggs in simmering water for approx. 8 mins., drain, rinse briefly in cold water and peel. Pour the beetroot juice into a bowl. Place the eggs in the beetroot juice and soak in the fridge for approx. 1 hr.
In a small bowl, combine the yoghurt with all the other ingredients up to and including the pepper.
Drain the eggs, slice in half, serve on a platter with the vegetables and the dip.