In a small bowl, whisk together the vinegar and mustard. Whisk in the walnut oil, drop by drop. Season the vinaigrette with salt and pepper. If acid is needed, add lemon juice. If more oil needed, add olive oil.
Tear the greens into large bite-size pieces in a flat bowl. Add the nuts and dill. Just before serving, add only enough dressing to coat lightly when tossed. Toss and serve.