Preserved Lemon Vinaigrette: In a mixing bowl, stir together all the ingredients. Season, to taste, with a little more salt and some pepper.
You should have about 1 cup of dressing. Set aside. You should have some bigger, thicker pieces of hearts of palm, and some smaller, thinner pieces. Put the bigger pieces of the hearts, in a non-reactive dish and cover them with 3/4 cup of the Preserved Lemon Vinaigrette. Cover with plastic wrap and marinate in the refrigerator for 2 hours. Drain the marinated hearts of palm and wrap each piece in a piece of ham. After the pieces are wrapped, cut them into 1/2-inch thick rings. Slice the larger pieces into 1/4-inch thick rings and set aside.
Drape half of each serving plate with the remaining Parma ham.
In a mixing bowl, toss the mesclun with the sliced small hearts of palm, 4 teaspoons of extra-virgin olive oil and season, to taste, with salt and pepper. Mound some of the greens in the center of each serving plate. Place the ham wrapped rounds around the salad. Drizzle the remaining lemon vinaigrette around each plate and garnish with the julienned Preserved Lemon Peel. Serve immediately.
Use a sharp knife to cut each lemon lengthwise not quite completely into quarters, starting at the flower end and leaving the quarters attached at the stem end. In a large, non-reactive mixing bowl, stir together the salt and 1 cup of the sugar. Add the lemons, toss to combine them evenly with the salt-and-sugar mixture, cover with plastic wrap, and refrigerate, stirring occasionally, for 30 days.
Bring the remaining 4 cups of sugar and the water to a boil in a large saucepan, stirring occasionally. Remove from the heat and set this simple syrup aside.
Remove the lemons from the sugar-salt mixture. Place them in another saucepan of enough cold water to cover them completely. Bring the water to a boil. Drain off the water and repeat with more cold water. Repeat again twice more for a total of 4 boilings and changes of water. Drain again and add the lemons to the pan of simple syrup. Bring to a boil. Remove from the heat, let the lemons cool in the syrup, and then remove and discard everything but the yellow-colored outer rind of the peel. Refrigerate in the syrup for up to 1 month, covered.
The preserved lemon peel will keep for 1 month covered in the refrigerator, and can be used in any recipes that call for lemon juice or zest, or can be diced and tossed with cooked vegetables.