Peel the potatoes and cut into quarters.
Peel and slice the red onion into very thin rings. Put them in a bowl of cold water for 5 minutes to remove the bitterness. Drain well by squeezing lightly between your hands. Pat dry with paper towel.
Cut the cucumber in half lengthways and remove the seeds. Sprinkle with 1 pinch of salt and leave to disgorge for 10 minutes. Squeeze between your hands to remove excess water.
Peel the carrot, cut it in quarters lengthways and then into thin slices.
Mix all the seasoning ingredients together in a small bowl.
Put the potatoes into a large pot and cover with water. Bring to the boil and cook for 10 minutes, until they are tender when poked with a knife. Add the carrots 2 minutes before the end of cooking, then drain.
Put the potatoes back into the pot along with the carrots and heat for about 30 seconds over medium heat, stirring the pot to allow the moisture to evaporate. Remove from the heat.
Add the seasoning and onion while the potatoes are hot. They will absorb the flavours of the seasoning and cook the onion slightly. Leave to cool.
Add the cucumber and stir in the mayonnaise. Season with pepper, then taste and adjust the seasoning as needed.
