Boil the potatoes. Cook the potatoes in a large pot of salted boiling water until tender, around 10 minutes. They’re ready when a knife slides into a piece with no resistance in the centre.
Drain and mash. Drain the potatoes and transfer them into a large bowl. Using a potato masher, mash until mostly smooth, stopping while a few pieces are still visible so the texture doesn’t turn gluey.
Season the hot mash. Stir through the dashi seasoning and rice vinegar while the potatoes are still hot, which is when they absorb it. Keep stirring until you can’t see any grains of powder left.
Cover and chill. Cover the bowl and refrigerate the potatoes until cool. Don’t move on while they’re still warm, or the mayonnaise will split in the next step.
Fold in everything else. Once cooled, add the eggs, corn, onion, carrots, ham and mayonnaise, and mix until combined. Fold rather than beat, so the mash keeps the texture you built.
Serve. Serve immediately.