Wash the potatoes and cook them for about 15-20 minutes in deep, lightly salted water. Check they are tender with the point of a knife.
While the potatoes are cooking, peel, halve and slice the onions. Warm the oil in a shallow pan, then add the onions and cook until soft and golden. Take your time over this – it could take as long as 25 minutes – stirring them regularly.
Peel the jerusalem artichokes and slice them thinly – no thicker than a pound coin. Add them to the onions and continue cooking until soft. Don’t worry if they break up a little.
As the onions and artichokes continue to crisp, break up the hot-smoked salmon and tuck it among them. Add the potatoes to the pan, breaking each one slightly with the back of a spoon as you do so, to crumble somewhat.
Chop the dill and parsley, and blend with the olive oil using a food processor or blender until you get a vivid green dressing. Trickle over the hash and serve.