Although fresh mackerel can be hard to find, smoked mackerel is often sold in the refrigerated section of supermarkets; it is also available from mail-order sources. We used the peppered variety, but any type will do.
Place potatoes in a small saucepan, and cover with cold water. Bring to a boil; reduce heat, and simmer until tender when pierced with a fork, about 12 minutes. Drain in a colander; let cool slightly. Slip off skins; discard. Cut potatoes into halves or quarters, if desired.
Meanwhile, make dressing: In a medium bowl, combine shallot, vinegar, and mustard. Whisk in the oil until emulsified. Sprinkle dill into bowl.
Add cucumber and cooked potatoes to the dressing in the bowl; season with pepper. Toss to coat evenly. Divide salad among four plates; arrange mackerel on each. Serve, garnished with greens.