1. For the vinaigrette, whisk all the ingredients together in a small bowl. Set aside.
2. Using a sharp, serrated or other knife, cut off the top and bottom of each lemon to expose the flesh. Stand each lemon up on the cutting board and carefully cut away the skin and bitter white pith in strips, working from top to bottom and following the natural curve of the fruit. Trim away any remaining pith.
3. To remove the lemon segments (suprmes), work over a bowl and cut down along the membranes on either side of each section to release it, letting the sections drop into the bowl as you go. Cut each segment crosswise in half.
4. Combine the arugula, parsley, and dill in a large salad bowl. Add the lemon segments, then toss gently with just enough vinaigrette to coat. Scatter the chive batons and parmesan shavings over the top and serve.