Bring a big pot of water to the boil and throw the samphire in. Blanch for around 6-8 minutes and then drain and immediately refresh in cold water. Separate any of the woody stalks and discard.
In a small pot boil some salted water and add the broccoli and samphire, simmering for two minutes. Drain the broccoli and samphire, cooling it down immediately with cold water and leaving aside.