Preheat the griller to the highest setting. To make the dressing, peel and finely chop the shallot, or trim and finely chop the spring onions, and place in a small bowl. Chop the dill or celery leaves and add to the bowl along with the vinegar, walnut oil, salt and pepper. Mix well and put aside.
Grease the griller tray with half the vegetable oil and place the trout fillets on top, skin side down. Season with salt and paprika. Grill the fish for 5–8 minutes, on one side only, until the flesh is opaque in the centre and delicately brown at the edges.
While the fillets are cooking, heat the remaining vegetable oil in a small frying pan and gently fry the walnuts, shaking and stirring constantly so that they colour but do not burn. Drain on paper towels, then chop roughly.
Rinse and dry the salad greens and arrange on four plates. Place a fillet of trout on each. Stir the dressing, spoon it over the fish, and scatter the walnuts on top.
Tiny new potatoes go well with the clear flavours of this dish. Put them on to boil before you start grilling the trout.